I think everyone should be asking "Why do I think the end game is boring?" before they go about hypothesizing about how much random events would fix that.
Fact: the end game is boring because, as another poster also mentioned, you're comfortably winning.
In that case, what the heck would random events do? If you're already comfortably ahead, then random events would simply be an annoyance that you deal with quickly. If you're neck-and-neck with your opponents, then random events provide an exogeneous swing factor that could make or break your game - and that's not my idea of fun... playing for several hours to be in a competitive state with my opponent only to have the game won or lost simply because of the random number generator in the game.
If you're considering a random event that is significantly swingy enough to make a comfortable lead into something worthy of attention, then that is TERRIBLE game design. Because that means in any appropriately-difficult game, the end game will be decided not by your skill, but by a cascade of random events.
The fact of the matter is is that Civ 4 is a game that rewards long-term skill. Adding greater levels of variance will only undermine it. Sure, one could argue that there's already a bit of luck when one considers the randomness of terrain and the placement of luxuries, and that combat is all about luck. However, in the first case, dealing with randomized terrain and random luxury placement is the test of skill that makes civ 4 a great game. Random events in the end game cannot have this impact for reasons that I already described.
In terms of combat, yes, while an individual conflict has alot to do with luck (as anyone who lost a fight with 99.6% odds of winning can attest), an entire game's worth of fighting represents inevitability. Put another way, if every conflict you have has 50% chance odds of winning but you have exactly the same number of troops as your enemy, then if you win the entire war, then that was due to luck. Because guess what? The next war in which you do the same thing or in the next game you play in which you do the same thing, you could just as easily lose. That's luck. However, if every conflict you have has 50% chance odds of winning, but you appropriately have twice the number of troops or more than your enemy, then if you win, that was due to skill. Sure, you may have a freak game in which all your troops die to a lone, fortified spearman (although anyone with skill would've known when to stop the war and rebuild), but the 99.9% of other games you play with that strategy will result in a victory. That's skill.
As such, random events in the end game can only add a limited amount of variance. If you add too much, then you marginalize the importance of skill. If you add too little, then all you do is make it more annoying for people with enough skill to have comfortable leads and make skill more irrelevant for people who only have enough skill to make games close. And there is no such thing as a "sufficient amount" of late game variance, because just the idea of late game variance undermines what makes Civ 4 great.
Remember: why do you like Civ 4 more than Civ 3 (if you do at all)? For me, among those reasons are the fact that I don't have to rely on the emergence of a Great Leader to finish a Forbidden Palace thanks to rampant corruption levels, the fact that I don't lose an army of tanks to a fortified spearman on a mountain, the fact that some of my key cities are absolutely devastated because global warming (despite the fact that I, personally, have dealt with pollution as best as I can) turn key, productive/food healthy tiles into desert at an escalating rate, or the fact that I can't build an Ironworks in a city that actually has decent shield production because it doesn't have the right resources in its borders, etc. I like Civ 4 because it, much more so than Civ 3, is a guarantor of skill. If i outskill my opponents, I am going to beat them in the end and not have alot of my game circumstances be ruled due to chancey events.
As someone else suggested, if the end game is consistently boring that you're considering random events to "spice" things up, just up the difficulty. If you are getting demolished in the early game in that new difficulty, consider it a new challenge to work your way up and become a better player. Because I guarantee you that no one here has a comfortable lead in a perfectly normal Diety-difficulty game.