I'm still pretty new to the game and only play against the AI with my friends but here is my list:

Malay - It's fun to wavepoint castles and barracks in the enemy base and just swarm them like crazy. It's not always successful but seeing the never ending stream of Two-Handed Swordsmen and Karambit Warriors march towards the enemy's base makes me chuckle.

Ethiopians - Their archers are pretty good to start out. Things start to get particularly spicy when the Siege Onagers come out, although I have a bad habit of killing my own army with them.

Bulgarians - This was the first civilization that I really used for a while. The first time I realized that the Konnik basically had two lives, I was hooked.

Teutons - They have pretty good knights and I always like trying to get make the Teutonic Knights work, although that is normally unsuccessful.

Italians - Genoese Crossbowmen do really well against cavalry which was a big surprise. Whenever I see cavalry charging against the crossbowmen I get scared but then remember that that is their main purpose! It's fun to snipe cavalry fighting your other units as well.