I'm with Tim in that I do consider diplomats and spies to be a part of my military effort - much the same way I consider engineers who help with road and rail building for my military. If you are able to take out a civ's capital with units by force, the remaining cities can usually be bought rather cheaply (unless the civ has the cash to move the capital or they are in democracy)
While some consider this "cheesy" or at least less than challenging, it is the best way to assimilate cities into your own civ by far and well within the rules of the game. You lose much less in the way of improvements and population in the target city and you will normally "inherit" built-in defenders. Combined with Leo's, this can provide a rock-solid defense.
When I do use my military, there are usually only a few times I'll go into all-out war:
1. Very early to clear a continent (like to use chariots, horsemen and elephants - the two-movement units that Tim mentioned).
2. If I have monotheism quickly (which I strive to do), Crusaders are good attacking units and I will use them to weaken or remove pesky civs that have not discovered gunpowder yet. In much the same way, if you are first to steam engine then ironclads will win just about every battle against defenders in coastal cities.
3. In the mid-game, If I am able to get bunches of cavalry units from Leo's then I may try some strikes. However, at this point the AI has uaually stolen or discovered gunpowder and built city walls everywhere as well. Often times it's better to wait unti:
4. Robotics. Once I have howitzer capability it's time to crush any civ left standing.
If you concentrate soley on military, it is quite possible to win the game by conquest quite early. Reading some of the reports from people playing GOTM #3, there are people who are winning the game before 1000 AD (and it's on emperor level as well - though it's on a regular-sized map and not a large one)
------------------
Diplomacy - the art of
saying "Good Doggie"
until you can find a rock
[This message has been edited by Kev (edited April 24, 2001).]