Kaiba, I am by no means the best player on this board. I am probably in the bottom 10%, but I like to hear my self talk so here goes:
On the lower levels, I like to do what you do, going straight from despot to Republic. However, from king level up, it is much better to switch to monarchy first. In republic, you pay 1 shield for every unit except for camels and diplomats, which really slows down your advancement. This is a real problem at king+, because in republic you cannot squelch unhappiness with martial law, and your cities cannot get very big (the fourth citizen of each city starts out unhappy on king, 3rd on emporer, 2nd on diety) until you build some 'happy' improvements, typically temples, market places and coloseums. So on these higher levels, you are best served by going to monarchy, where the first 3 units supported by each city are free. Plus, you can get one more content citizen for each unit in a city, so you can grow your cities a little more freely while you crank out some early wonders and the 'happy' improvements. It also allows you to explore a little more freely.
Once you switch to republic, you have only one goal: to make your cities grow, fast. As noted, you need happy improvements. You need to be prepared to rush build mikes chapel and bach's cathedral as they become available. This is really important with Bachs, because theology (the tech which allows it) cancel's the Oracle (if you built it, and it really helps in higher level games). SO you have to make Bachs come on line the turn after you get theology, so the "cathedral in every city" can replace the "+2 content in each city w/ temple" from the oracle.
Once in republic, turn up the luxuries. In each city where more than half of your citizens are happy and there are no unahppy citizens, that city will hold a celebration day. The celebration will continue until an unhappy citizen appears or you lack the luxuries to make half or more happy. Each day a city celebrates under republic or democracy, its population grows by 1. This allows you to build very large (relative to the level of the game) cities early in the game.
Some time during this, I like to switch to Democracy. I like to build spaceships, and democracies, with the extra trade, celebration days and no corruption or waste, is by far the fastest way to develope new technologies.
If you prefer conquest, I still would suggest democratizing for a while, specifically until you develope mobile warfare. Democracy trade/tech advantages will allow you to develope a new tech every couple of turns, at least. You can then use the statue of liberty to switch to commy or fundy and launch a world wide campaign. You will have tanks, battleships, transports (and pretty soon, stealth aircraft, howitzersand huge cities which can pump them out at an amazing rate.
Note that you can conquer the world as a democracy. I do this by building shakes theater in my best shield producing city. Then I use my railroads to move all new units on that continent to the shakes city and support them from that city. Since shakes suppresses all unhappiness, these units can move around freely. With industialization, you can support at least 50 and eventually 100+ units out of such a city. The challenge becomes 1. get the ai civs to declare war on you. 2. Conquer them completely before they can sue for peace.
The Anals of Rome timeline on the Civ2 timelines page gives a great description of how to do this.
