How long do you think Western civilization will last?

I think you need to define 'Western Civilization' a bit better, along with what counts as 'lasting' if we're to have a detailed discussion. Nonetheless, it's an interesting topic to think about, especially at this point in history.

In more vague terms, the first things that needs to be considered us global warming as it obviously affects the 'lasting' of humankind. If I had to put money on an outcome, I think that we will probably be able to avoid many of the worst-case scenarios but not before reaching a point where the global environment is significantly changed. So it follows that I doubt that will be a direct cause of the end of Western civilization, but it's certainly a possibility that needs to be taken seriously in how we act today.

The second thing to consider is global geopolitics. I also don't think that a full-scale thermonuclear war is likely to occur in a global sense - at worst something might happen in NK eventually but I think all of the major global powers realize that there will be no winners once people start pressing their red buttons. However, on current trajectories the USA will wane in its global dominance, slowly being overtaken as global leaders by China, Russia and potentially Brazil and India if they play their cards right. Potential for this not to happen is there, but very unlikely unless the US gets its act together soon (IMO starting with reform of its electoral system, but that's a topic for another thread). This doesn't mean that 'Western' countries and cultures disappear, but they become less relevant on the global stage, and smaller countries formerly significantly 'Western' may well find themselves choosing to re-orient towards the new global leaders, especially if they aren't geographically close to the existing hubs of North America or Europe. This could happen as soon as 30 years if the right global events occur (especially conflicts between superpowers), or it could take hundreds or even not happen at all if the right permutation of situations comes to pass - it's really a fool's errand to try to put a number on it.

The final major consideration in my view is the interplay of the above two points. Resource scarcity caused by global warming (primarily water, secondarily food, and to a lesser extent consumables like oil, coal and fertilizers) combined with unstable geopolitics and zero-sum opportunism will almost certainly see more localized conflicts breaking out with a good chance of becoming proxy wars. Again, not likely not completely extinguish the West, but also not at all doing it any favors if it is in decline.

Ultimately, I think assuming that mankind doesn't any anything remarkably stupid on the whole that Western civilization will definitely be observable in some form for a good few centuries at least but eventually may merge and be supplanted with something more noticeably resembling that of the developing powers. I don't think there's much more of a solid answer to be given, really, because so many of the choices that will be made in the short-term can and will have massive impacts on the shape of the world and the human race a hundred years from now, so talking any longer-term is almost pointless. I truly believe that with the challenges before us at the moment the people alive today in functioning democracies will have more of an impact on the fate of humankind than any generation past or coming any time soon.

What is "Western civilisation"? In one sense, it has lasted for about 2,000-2,500 years, if we trace it back to its roots in classical Rome and Greece (I'm sure a more knowledgeable historian might able to demonstrate a continuity with the ancient civilisations of Babylon and Egypt, giving us an even longer existence).

Different empires might rise and fall, but the concepts of democracy, secularism, and science have lasted continuously for that long. In that context, the fall of modern-day regimes like the U.S.A. and the European Union will be just blips, as they're succeeded by other regimes carrying the torch of "western civilisation".

I think the biggest threat to our civilisation is environmental, rather than political or technological. We're changing our environment in so many ways and so quickly that we may not adapt. Also, many millions of people (possibly billions) will be displaced as the areas of our planet which are habitable change and shift. There will be natural disasters. There will be famines. There will be wars.

However, there will still be people. Even if our population is greatly reduced, the remaining people will survive (somehow!), and will carry on the traditions of our civilisation - even if our successors are as different to us as we are our predecessors.