Someone mentioned how the AI manages to always build spearmen repetitively. Most of the time, they aren't building them in that city. They are moving them from the back undefended cities to the front lines to defend the capital or the important city. That's why it's important to attack with strong numbers at three different points, which might seperate your forces, but also seperates their own defenses... and usually, they ludicrously overestimate your attack and rush to defend the city, only to find out the two horsemen you sent there did not one damn thing of damage.
Usually, I attack with the idea of seperating their military forces with two "faulty" attacks with a fearable amount of men at way backwater edges of their civilization... seperating the defense and offense forces in two, away from the center point of attack... than, I move in with the true army, about 20 horsemen, 20 catapaults, 6 swordsmen for weakening them for horsemen to attack easier and maybe even a few warriors to cover my army from what little offense is left to stop me.
With the forces divided, I use the remaining units from my dunce attack to pillage roads around the cities. Pillaging is the most effective during ancient times, due to the reliance on expansion and happy citizens during that time. Also, cutting off the resources and defending them from enemy attackers is effective.
With the centerpoint of your attack within your grasp, preferably being the capital of the civilization which you proclaimed war on, use this as an area to heal your units between fighting the divided empire, and as a station to put more into. Your first priority should be to quell resisters, then move on and find another good couple of nearby cities to rest as well, garrenteeing your not culturally overthrown and lose all of your military units in healing (it's happened to me multiple times - it sucks).
With the empire divided by the center occupied friendly territory in your pocession, the use of diversion forces and the pillaging of roads connecting the two sides of the empire, you'll find it much easier to be a military genious during the ancient era. Now, just wait for that medeival, unique unit infested age and pray. ;-)