Does the number of cities tend to have much of an impact on your economy early on in the game? Or do you find this number to be rather meaningless, so long as you can quickly research code of laws, currency...
This is great stuff. Much appreciated.
The number of cities is pretty much the
only thing that has an impact on your economy early in the game. The number of cities you have and the distance each city is from the capital determines how much you pay for city maintenance. The total number of cities and your total population determine how much you pay for civic upkeep. Together, these two expenses are going to suck up the lion's share of your money...at least until hyper-inflation and corporation costs kick in during the Modern Era.
Check out the Financial Advisor (F2) to see where your money is going. You can hover your cursor over the City Maintenance and Civic Upkeep entries to get a further breakdown of costs.
In this sort of situation, your top priority tech should be Code of Laws. This allows you to build Courthouses and run the Caste System civic, which in turn lets you run Merchant specialists in your food-rich cities...basically, trading in production and science for enough gold to keep your economy afloat.
But your main problem appears to be overexpansion. It's true that land is power, but only if you can work it. If your upkeep costs are causing your units to go on strike, you're slowing down the rate at which you can effectively work (and defend) your new territory. More importantly, you're choking off your tech rate, which can only hurt you in the long run. It takes longer to discover the techs that allow you to build courthouses, markets, and grocers, which retards your economy, which hurts your tech rate, and so on. It's a vicious cycle, and on the next continent over Mansa Munsa is quietly preparing to bring civilization to your primitive people at the point of a bayonet.
I'm probably on the conservative side when it comes to expansion, but I never build more than three or four cities. Unless I'm forced to go to war for horses or iron, or if somebody builds a tempting wonder or shrine near my border, I don't go to war until at least catapults and swordsmen, more often trebuchets and macemen. I almost always control my entire continent by the time I discover Astronomy, but by concentrating on my infrastructure in between wars, my economy doesn't suffer.
If you want to continue your current habits, one or more of the following is absolutely essential:
1. Playing an Organized or Financial leader will give you some wiggle room in your economy. To get the most out of the Financial trait, though, you've got to spam cottages like nobody's business.
2. Get religion, son. Founding a religion or nicking somebody else's Holy City are equally valid options, so long as you can generate the Great Prophet to get that shrine up. Shrine income goes directly to your treasury, so its importance to an expanding empire can't be overstated.
3. If you can't get your hands on a shrine, you can rig up a poor man's version using an enemy capitol. Capitols tend to be food-rich, making them perfect Great Person Farms. Maximize the city's food output, switch to Caste System, slap up the Globe Theatre ASAP, and run nothing but Merchant specialists. Settle any Great Merchants that appear. The cool thing about this city is that Great Merchants provide +1 food to whatever city they settle in, allowing it to grow larger, allowing you to run more merchants, giving you the cash you need to take over your next neighbor. It's like a perpetual motion machine of filthy, filthy lucre.
The Civ IV economy is an extremely complex animal, and a number of very smart people on these boards are still debating it. You might try keeping it small in your next couple of games and see how that treats you. Otherwise, that's about all I got.
Edit: Wow, that post sort of got out from under me. Apologies for the textwall, and feel free to ask for clarification on any semi-coherent, rambling point.