I like to fight wars. I have since Civ 1. I just like it.
That said, I'm usually pretty peaceful, fighting mainly when attacked. Civ 5 especially becomes pretty draconian when you start wiping civs out. On the rare occasions when I still go for military victories, I usually build until someone attacks me. Then I mobilize an army and anihilate them (much harder to do in Civ 5. Now, I usually have a military city very early on.). This gets one of my friends mad at me, so they attack me, and I kill them.
Soon, I'm fighting the whole world because Alexander tried to take me down. That gets very annoying.