People mention late-game tedium a fair amount. The complaints fall into two categories: frustrations with having to micromanage a whole bunch of things in the lategame, and annoyance with being in a position where the game is basically won (as in, none of the other AIs/players have a reasonable chance of beating you), but it would still take a bunch of time to achieve any of the victory conditions. These suggestions are tailored more toward addressing the second set of issues.
The first thing to ask when looking for a solution for this problem is - how do you get in a position where you have essentially "won" but are still far from any of the victory conditions? The answer is, you build up enough of an economic, research, and/or military lead so that even if all the AIs teamed up on you, you would still wipe the floor with them. Achieving such a lead requires passing through a region where you are recognizably a serious threat, but are not yet unstoppable, and not being contested by enough of the AIs to get your snowball halted.
Let's look at an actual GalCiv3 example. I got a very good map draw - starting in the middle of a fairly large star cluster, while my 3 opponents started off in smaller star clusters off to the edges. As a result, I was able to get to over twenty colonies, while the AIs only had 4-6 at the end of the expansion phase. Now, if the AI were playing to win, they would have immediately identified me as a serious threat, and started cooperating while preparing to attack. Instead, they sat around doing nothing while my econ exploded - the only reason I haven't finished it by now is because I'm still testing stuff out.
AIs should be on the lookout for potential runaway civs (they could use certain milestones, like "has 30% more researched tech points than anyone else", "has 33% of the military power in the galaxy" or "has 45% of the population in the galaxy"). Once a player passes a "runaway snowball" milestone, the AIs each choose between two options: "This player is getting dangerously strong, I'd better form a coalition to take them down!" or "This player is getting powerful, I'd better team up with them!"
Thus, once you start getting powerful, the game progresses naturally into a fight with you and your hangers-on vs. the rest of the galaxy. If your enemies fail to weaken you enough that you fall below the danger threshold, they start becoming increasingly desperate - doing things like setting research to 0, producing nothing but military units. If the game lets you go into debt or take out loans for speed-buying, they do that too. If that fails too, they surrender, ending the game.
This would make the endgame a lot more interesting than hitting End Turn a bunch of times until you win, when there's never any chance of defeat. Admittedly, it would make Tech and Ascension victories a bit rarer, as you would have to achieve the victory threshold before your opponents spend everything trying to stop you and surrender. But then, holding the line vs. a massive enemy assault is more interesting than how those victory conditions tend to play out right now.
So, would anyone else like to see this?