I find the early and mid-game great fun: there's excitement and challenge as I explore the world, found cities, and challenge the other players. But then the end-game almost always turns into mind-numbing slog.
For example, right now I'm playing 8-player vs. AI. I've reached the point I always seem to reach: it's basically inevitable that I'll win now, but I still have to give repetitive orders to tens of cities for a hundred or more turns to wrap it up. I go in hoping for an interesting victory condition, but I usually fall back on Conquest since that ends the monotony a little quicker.
A friend of mine has the same experience. Are we doing something wrong, or do we just lack the needed patience? Are Civ end-games usually longer and less challenging than the openings?