Edit: Wow, this turned out to be a long comment. tl;dr - you can change playstyle to cut 50-80% of the time off your Civ IV games and play them quickly. It's my favorite game, so here's a long comment that'll really only make complete sense for Civ players.

Civ IV is one of my favorite games, and I used to have the same problem - games took forever. But, you can drastically speed up games by changing settings and playstyle.

Generally:

1. Less land
2. Less ocean
3. Less civs
4. Less space
5. Higher difficulties

are conducive to a faster game. Yes, higher difficulties, because you'll lose early fairly often, and the games where you don't lose stay very stimulating and exciting. Mid/lower settings mean you'll win more often, but it's slow and boring at the end after you've got a dominating lead. Playing out the endgame becomes rote.

Also, the way you play changes it. Later wars and offensive wars take more time. If you war early and wipe out the nearest Civ or two near you between axes, swords, elephants, and catapults - the pre longbow wars - they go pretty fast, then with the extra space you can build out without fearing war very much for the rest of the game.

Alternatively, defensive wars where you use defensive units and let yourself be attacked go faster.

Finally, smaller, better utilized empires can mean less playtime. In Civ IV you have a big tradeoff with the exponential growth cost of cities. That means you can choose between trying to aim for a 9-12 city late-game before you go on a rampage, or the "as many cities as possible" way. But really, 9-12 very good cities and razing the rest of the enemy cities plays a lot faster. There's a lot of mediocre cities that "break even" on their contributions to research/production of their cost. You can simply not take them at all, just don't found them, or burn them down if you capture them. That said, this is conducive to different buildings, civics, and playstyle. Bureaucracy becomes much more powerful, State Property is weakened. Courthouses go from first priority with a larger empire to a nice "if we've got free time" sort of thing. If you're playing a smaller empire, you have less frontier/border cities, so it's easier to build walls and castles to fight a defensive war if/when you get invaded. Etc, etc.

My Civ IV games used to run 30+ hours. With a different playstyle, I can now usually see if I've got a reasonable chance to win within 2-6 hours, and then I'm looking at maybe 4-5 more hours of pretty exciting endgame if so. And I micromanage my production and wars quite a bit - if you don't mind using the "optimize xyz" options that get things 90% right, you can bang out a pretty good game in 3-4 hours. Compare that to my old way where the game was decided after 10-15 hours, and then you're looking at 10-20 hours of boring "cleanup" where you slog along to victory and... yeah, I like it much better this way.

Edit: A good way to learn to play fast games that teach you a lot is to go Duel-sized map, one random opponent, opponent, Deity difficult, and be one of the Civs with a good early war unit like Persia or Mongolia. Make 1 or 2 cities, hook up horses/copper/iron, and try to take the other side out. It's harder than it sounds, and it'll be a one to two hour game. You'll learn more about higher difficulties, early build priorities for fast wars, and using terrain and prioritizing in combat. The computer has such a production edge that you need to play the tactics very well to slow them down, put choke points in their land so they can't hook up metal for the counter to your unit, and so on. Similarly small map/high difficulties/gear towards winning or losing early makes fun games while teaching specific skills.