Which covers did it better than (or put a fresh twist on) the original?

I'll get the obligatory ones out of the way:
Johnny Cash - Hurt
Jeff Buckley - Hallelujah
Cyndi Lauper - All Through the Night
Whitney Houston - I Will Always Love You

Edit: How could I forget:
Disturbed - Sound of Silence

There is a Korean program called Begin Again which brings in artists to perform different versions of their own songs and covers of other groups and individuals. Often times, they will pair singers from different generations, and artists who have never worked together before. It's always high quality.

Here are a couple of favorites:

Wheein singing Dimple, originally by BTS. This is a very different take on the song, with an R&B flavor.

Solar and Navi singing Drowning Original song by Woodz. The power in their voices is just astonishing.

Edit: Fixed second link.

That 3rd-wave ska really churned out a lot of bangers

Save Ferris - Come on Eileen
Reel Big Fish - Take On Me (They have a ton of great covers if you want to burn an afternoon)
Alien Ant Farm - Smooth Criminal (not ska, still baller)

And the one that I well and truely love more than the original:

Goldfinger - 99 Red Balloons

Well there’s Obadiah Parker’s Hey Ya.

And in a similar but funnier vein, Alanis Morisette’s take on My Humps performed as a torch song.

And finally, Megan Washington, has an entire album that is a cover of the Killers’ debut album Hot Fuss

Hurt - Johnny Cash was such a great twist on the original. Really well done, and you could see in the video how much it meant to him to get this out.

I'm not a big fan of lightly done cover versions and particularly dislike them when it's an artists one trick. Think pentatonix, that baritone clown bloke, etc.

Once you look to the folk tradition things start actually having some vitality though and you can make an argument folk music almost is cover versions, just owned and morphed and digested to a point that the term is a bit of an insult. And in folk I'm happy to include blues, country and so on. Sometimes even things like hip hop, which can piss people off.

I'm ignoring "better" here and going with "owned it" instead.

In that vein have a look at most of the Mary Wallopers output. See if you can pick which songs they did write.

The Irish Rover by the Pogues and Dubliners, live. It'll give you whiplash.

In my book it's a folk album - Nirvana Unplugged. The whole album is great and has many covers, once again you wouldn't know if you weren't familiar with the songs, but where did you sleep last night is extraordinary.

Hallelujah by Jeff Buckley.

This is the just woke up before coffee random thoughts. I'll mull on it.

Tina Turner's cover of Proud Mary is excellent. Starts off nice and easy, then totally pops off halfway through the song

Honestly, I end up listening to remixes more than I listen to covers, but it's always remixes that I end up preferring over the original version. But there are covers I enjoy as much as/more than the originals.

Remixes
Tom's Diner by DNA | Original by Suzanne Vega
It's A Fine Day by Opus III | Original by Jane / Technically a remix of a spoken word poem than a song
19-2000 (Soulchild Remix) by Soulchild | Original by Gorillaz
Bang (Peanut Butter Wolf Remix) by Peanut Butter Wolf| Original by Malenas

Covers
Brown Eyed Girl by Everclear | Original by Van Morrison / This is... not a full cover. It's kind of a reminiscence of the song itself?
Mad World by Gary Jules | Original by Tears for Fears / Gary Jules' version sticks with me for its use in Donnie Darko, but generally I actually listen to the Tears for Fears version.

Editing to add a blurb from the Wikipedia article on MP3:

An acapella version of the song "Tom's Diner" by Suzanne Vega was the first song used by Brandenburg to develop the MP3 format. It was used as a benchmark to see how well MP3's compression algorithm handled the human voice. Brandenburg adopted the song for testing purposes, listening to it again and again each time he refined the compression algorithm, making sure it did not adversely affect the reproduction of Vega's voice.[47] Accordingly, he dubbed Vega the "Mother of MP3".[48] Instrumental music had been easier to compress, but Vega's voice sounded unnatural in early versions of the format. Brandenburg eventually met Vega and heard Tom's Diner performed live.

To name some less universally known picks to complement the classics above:

• Spiritualized's cover of Elvis' I Can't Help Falling in Love with You may stretch the definition of cover as it's more its own song, but it's still potentially the most beautiful piece of music recorded this century.
• Lankum's take on the Specials' Ghost Town is a whole new song too. What a journey!
• Girl Band (now aka Gilla Band)'s rock cover of Blawan's EDM bop Why They Hide Their Bodies Under My Garage? is an ugly wonderful monster. Linking the live version but it's killer in the studio too.
• The incredible Kiran Leonard covered The Tammys' gorgeous early 60s pop song His Actions Speak Louder Than Words with a gorgeous rock band of unconventional instrumentation for years; I'm glad a live recording was finally recently released. That haunting outro...
• And then there's Jim O'Rourke's epic rendition of Tracy Chapman's Fast Car... a half-hour journey that never gets old.

Halo - Ane Brun

Rage Against the Machine Ghost of Tom Joad

I also love the original.

I'm a fan of Richard Cheese, who does jazz covers of "inappropriate" music like various metal hits, lewd hiphop songs etc. Here's his cover of Creep by Radiohead and People = Shit by Slipknot, but the whole Sunny Side of the Moon album is excellent. Metal and jazz are two genres I've been listening to since I was about 7 years old, so naturally I love this. His style enhances the slight inherent silliness in metal that's trying to be super dark and heavy.

I'm also a big fan of Nomeansno who did a couple covers, my favorite and probably the most interesting and high effort one is Bitch's Brew, originally by Miles Davis.

I don't listen to a lot of these, but Kasey Chambers' cover of Eminem's Lose Yourself was absolutely amazing.

I really like the edge that was added in Escape the Fate's cover of Smooth (originally by Santana with Rob Thomas).

If you enjoy alternative rock and associated genres, the various "Punk Goes..." albums are worth skimming through. This one is my favorite though.

Pretty much every cover done by Chase Holfelder. I discovered him years ago from his Major to Minor covers of Amazing Grace and the Star-Spangled Banner, but every cover he does is amazing.

Two specific highlights off the top of my head: Major to Minor cover of Deeper from Moana, and Dance Monkey using toys. I actually heard his cover before the original. When I heard the original for the first time on the car radio with my dad, I was so disappointed by it and played Chase's cover for him afterwards.

One more awesome cover that's WAY too underrated: Rat, by LittleJayneyCakes. Another cover I heard before the original. Jayn's voice and the remixed instrumentals just really hit a good note for me, and the message resonates hard.

I'll leave it there because my next instinct is to start bringing up Vocaloid and other Japanese music covers which is very extensive. The cover scene is huge in both Japanese and English and people can put BIG spins on them, there's all sorts of metal and rock covers and remixes... Actually screw it, here's Kagerou Daze with a chorus of 50 singers and orchestral music. Yet again the version I heard first, and it's just so damn grand and powerful that the original has always felt pale in comparison.

If anyone wants more covers from that scene, I'd be happy to make a list xD

California Dreamin, by Eddie Hazel

Also, Bobby Womack's cover of it

My favorite that few have probably heard is a cover of Danzig's "Mother", by an artist who goes by "Lissie": https://youtu.be/hUmw2iYgFbs

Breathing and reminding myself that everyone's take is valid and that my musical tastes are just that, tastes haha. ;) I have my own hot takes coming it.

Country Road - Whitney
Just One Look - Derevolutions
Cold Hearth - Elton John et. all if it counts as it's quite the mashup.
Everyone's a Winner - Ty Segall

I Can't Cry Hard Enough by Victoria Williams. It's so good, you can't believe that she didn't write it.

Someone a few month's ago posted GWAR's cover of Chappell Roan's Pink Pony Club. Not a really a fan of Chappell Roan, nor GWAR, but GWAR's is great. Original || Cover

I have a lot in my collection but it'd just saturate the list, so here's some of my favorites.
I wouldn't necessarily say better, just different. And I love the fresh takes.

• I Will Survive - CAKE
• Faith - Limp Bizkit
• Karma Chameleon - Me First and the Gimme Gimmes
• Just The Two Of Us - Fanfare Ciocărlia
• Lo stregone (Witch Doctor) - Fred Buscaglione
• Like A Virgin (metal cover) - Leo Moracchioli
• Sexy and I Know It - Brett Domino
• WAP - Richard Cheese: feels more explicit than the original since you can understand the words better
• Follow Me - Max Raabe: I don't know why the video looks like that
• Respect - Otis Redding*

• This was the original and I learned this from Second Hand Songs, a website collecting covers!

And also, here's my somehow dated Spotify playlist of "Wrong Genre" Covers.

Cake - I Will Survive
Marilyn Manson - Sweet Dreams
Santa Esmeralda - Don't Let Me Be Misunderstood

... and probably anything by Joan Jett, because I believe her only self-written song I know is Cherry Bomb.

Edit: Totally forgot about System of a Down - Metro! Though, it isn't as unlike the original as the three above.

As a child of the eighties I offer up Grace Jones' cover of Roxy Music's song ‘Love Is The Drug’.

House of the Rising Sun by The Animals

Across the Universe by Fiona Apple

Doin Time by Lana Del Rey

Once Upon a Dream by Lana Del Rey

I prefer Purity Ring - Grammy over the original by Soulja Boy.

Honorable mention: I think Ariana Grande - Emotions is a very impressive cover, but wouldn't say it's better than Mariah Carey.

I'll add links to this later, but as for a twist on the original Easy Star All-Stars with their cover of the entire OK Computer album is up there for me.

*edit
Link added for anyone who wants to check it out
Easy Star All-Stars - Radiodread

There's some great ones in these comments, so I'll give one that's a bit more on the silly side (though still great IMO): Chance - Milkshake. The same artist also put out a cover of Prince's When Doves Cry that I love, but I haven't been able to find that on the internet anywhere to share.

I'll also shout out Rick Astley's covers on youtube.

Thought Miley Cyrus' cover of Jolene mentioned elsewhere is good, the White Stripes live cover is tops for me. Nobody puts more emotion in it than Jack White.

Also Dead Sara's Heart Shaped Box

Skinny love by Birdy

Devil Town by Bright Eyes

Panzeraballett - (I've had) the time of my life is a re-harmonized jazz metal version of the hit from Dirty Dancing.

I'm sure to have a few more to add later on, but for now I want to throw in a few from my personal kings of cover tunes:
Type O Negative - 'Summer Breeze' (Seals & Crofts cover)

• Type O have some excellent covers throughout their catalogue, and this is easily my favourite. You wouldn't expect the band who released an album called 'The Origin of the Feces' to cover Seals & Crofts, and yet in retrospect it seems a no-brainer. What's also remarkable is the wonderful transition into the next track on the album, 'Set Me on Fire'; the two songs gel beautifully and reinforce how well Type O integrated the song into their ironically morose brand of doom metal. I've linked above a version with the two together, as they should be.

Type O Negative - 'Angry Inch' (from the film 'Hedwig & the Angry Inch')

• I wouldn't have known about the film without this track, so this was a nice two-fer when it came out (maybe three-fer counting the musical, though I haven't seen that rendition). Fits their humour just as well as their musical style.

Type O Negative - 'Day Tripper Medley' (The Beatles cover)

• Type O weren't called the 'Drab Four' for nothing. The 'She's So Heavy' section fits them like a glove.

Common People - orla gartland and look ma no computer - https://youtu.be/ybE4flVt_q4?si=5F40u1XF0_MYu4ef

I asked a similar question a while back that got a ton of recommendations.

A few of my own favorites that come to mind:

Denzel Curry - Bulls on Parade | original by Rage Against The Machine
Feist & Ben Gibbard - Train Song | original by Vashti Bunyan
Killing Me Softly, by The Fugees, or Roberta Flack (the Frank Sinatra cover is just okay, IMO) | original by Lori Lieberman
T-Pain (and his fantastic band!)'s cover of War Pigs | original by Black Sabbath
Ben Howard's cover of Call Me Maybe | original by Carly Rae Jensen
Wu-Tang Clan - Sucker MC's | original by Run-DMC
Too $hort - I Need A Freak | original by Sexual Harassment

I'm sure there are more, but I'm quite fond of The Killers' take of Joy Division's Shadowplay and Shiny Toy Guns' take on Peter Schilling's Major Tom (Coming Home).

Slothrust cover of Pony there is also a fifteen minute version too if you never want that guitar solo to end

I'll add a couple:

• Paramore's cover of Passionfruit
• Peter Hollens feat. Tim Foust cover Sound of Silence

Thanks to everyone for contributing, I've found so many amazing takes of so many songs!

A mix of covers I enjoy ranging from label releases to small youtube creators

• Schneider TM & KPT.michi.gan, The Light 3000 - A glitchy idm cover of The Smiths - There Is A Light That Never Goes Out. My favorite cover
• José González - Heartbeats I have a soft spot for the original by The Knife but this an excellent and perhaps well known cover
• MEUTE - You & Me A Marching band style cover of Flume's remix of Disclosure - You & Me. These guys cover quite a few songs, this one translates well
• Moderator - Words Remain A trip hop-ish cover of Josh Garrels though iirc the original has roots in Jewish history
• Sticky Fingers - Delete Like a Version feels like cheating a bit here but this is my favorite from the series. Nothing complicated here, its a stylistic cover of DMAs - Delete
• Great Grey Buildings - Oceanographer's Choice A cover of The Mountain Goats. No Children gets all of the attention from Tallahassee but this song has always been a personal favorite and this version works for me when I want an alternative
• Erin Rae - Across the Great Divide A Kate Wolf cover that respects the original while applying the artists personal sound
• Kate & Janelle - Star Witness A Neko Case cover from my younger years. Its pretty faithful to the original but has the raw energy of a couple of kids jamming in a school stairwell
• Juliana Chahayed - What You Won't Do For Love - A cover of Bobby Caldwells classic. This is a frequently covered song, been a fan of this version for a decade or so
• Soft Cell - Tainted Love An 80s classic, Its fairly well known that this is a cover of Gloria Jones version from the 70s
• Israel Kamakawiwoʻole - Somewhere over the Rainbow This one is pretty well known but I didn't see it mentioned

Pupsi on YouTube does some pretty cool covers. He carves squash, gourdes, and other foods into instruments. You get to see the whole process, including tuning by carving more away. My personal favorite is his cover of Despacito by Luis Fonzi.

I prefer Counting Crows' "Big Yellow Taxi" to Joni Mitchell.

Way too many to mention all of them, but anyone from the UK should be well aware of BBC Radio 1 live lounge. For those that don't artists come in and do a small live set of which one song is always a cover, some of these end up becoming very well known.

Someone has very helpfully created a playlist of them from the official Radio 1 YouTube account

A few examples:
Harry Styles - The Chain (Fleetwood Mac cover)
Pendulum - Violet Hill (Coldplay cover)
Taylor Swift - Riptide (Vance Joy cover)
Adele - Promise This (Cheryl cover)
Amy Winehouse - Valerie (The Zutons cover)

My other post forgot to mention Peter Gabriel's cover of Heroes (originally by David Bowie)

Also the Nirvana Unplugged performance is basically entirely acoustic covers of rock songs.

For a ton of ska covers of many, many songs, check out SkaTune Network. Just click any of the videos, they're all great. (He's doing a polka thing for April, too.)

Off-topic... kinda?

So… I thought this topic was about actual album covers, as in the artwork, and my mind immediately started wandering through some of my favorite cover art. Then I started reading the comments and realized everyone was talking about cover songs instead…

But since I already went there in my head, I still kind of want to share a few album covers I love anyway in no particular order other than the order they come into my head:
Breach - Twenty One Pilots
Blurryface - Twenty One Pilots
Tourist History - Two Door Cinema Club
The Original Motion Picture Soundtrack - Saint Motel
saintmotelvision - Saint Motel
DDMN - SAINT PHNX

Ps: I can take this comment down if it's too unrelated to the topic but I thought it was kinda funny that my brain sidetracked like this.