lol I actually didn't think of this, you're right. But, is there a way to counter the waiting? Something I can do so that I don't have to wait no matter how long I'm in the game?
Well, you can't guarantee that you'll
never have to wait. But one of the most effective things in Civ3 is to disable air and sea trade. It turns out that a lot of the time the computer spends calculating is figuring out what the trade routes all. That's why you may notice that if you pillage a road, especially one containing a resource, in the late game with many, highly-developed, civilizations, it actually pauses for a few seconds. Think of all the AIs pillaging roads (or bombing them) during the AI turns - if there's a lot of wars going on, that really adds up. If you disable sea and air trade, however, the turn times will be much faster.
To change this you'll need to create a scenario with the Civ3 editor. Start up the editor, and click on the Scenario menu, and then click Custom Rules. Click OK to the warning, and then click the Edit button in the upper-right area. This will open an "Edit Civilization 3 Rules" window, and click on the "Improvements and Wonders" tab. Select "Harbor" from the "Improvement or Wonder" list (or hit 'H' a few times to get to Harbor), and you'll see a check box 'Allow water trade' in the middle area of the screen that is checked. Uncheck it. Now select "Airport" (or hit 'A' a few times to get to it), and uncheck the 'Allow air trade' box that will be checked. Now hit the "Close" button in the lower-right of the "Edit Civilization 3 Rules" window, and go the the File menu, and choose Save As, and choose a name for your scenario, say, "Less Trade.biq". Now, in Conquests, from the main menu, go to "Civ Content", and choose the "Less Trade" scenario (or whatever name you gave it). This will start up your new scenario, with much faster turn times.
Now, the downside is, if you colonize an island that has Saltpeter, you have no way to get that Saltpeter back home (although you could take the musketmen home on ships, or send pikemen out to the island to upgrade them, and bring them back). But you will be able to play with as many civilizations as you like and still have short turn times. Maybe not instant, but much faster than it currently is.
The other two options that make a big difference are the number of civilizations and the size of the map. Since you don't want to have fewer civs or a smaller map (and I agree, reducing those does make for a less dramatic game), eliminating sea and air trade is the only other option that's easy and has significant impact. You might be able to get away with just eliminating sea trade and still getting a good impact, too, at least until airports become commonplace, which doesn't happen every game. There is one more option, eliminating all building maintenance, that I've heard makes a significant difference, but you'd have to set the building maintenance to zero for every building in the editor, and that obviously would de-balance the game somewhat (I think most scenarios that do that counter it with high unit maintenance costs).
If you still aren't satisfied with the turn times, I'm afraid the only option is a faster computer. There's a thread in Civ3 Technical Support where a few of us have compared our computers' performance on the same, slow, savegame. What the results indicate so far is that the most important factor to look for on a computer is what is called the L2 cache. More is better. Intel processors also seem to do much better than AMD ones for Civ3 - a 2009 AMD processor running at 3.3 GHz did no better than my 2007 Intel one running at 2.2 GHz, which is impressively poor - most people would expect it to perform 50% faster. And the newest Intel processors are not necessarily the fastest for Civ3, because they have less of this all-important cache.
What's amazing is that apparently most people found the game ran acceptably back in 2001. Firaxis did downsize "Huge" from 180x180 to 160x180, and Large from 140x140 to 130x130, sometime between Vanilla and Conquests, though, probably because it was too slow at the bigger sizes. I think the only reason I found it fast enough was that I usually played with 8 or 9 Civs on Huge back when I first started playing, instead of 16.
Try eliminating air and sea trade, though. It should make a quite noticeable difference.