I like to play a more diplomatic game, going to war only when I have to.
One thing that really makes me mad, that sent me to war once in my current game is... I had an island, just off the coast of my main continent. The island was small, only enough room for like, 4 coastal cities and maybe another city in the middle. Well, I had some space between my borders, and here come the Sumerians, settler getting off their boat to take that unclaimed land. I hate when the AI does that, and it was the only time this particular game (one of the few, rare cases period) that I just went to war with a country.
Most of the time, the AI goes to war with me (i.e. they demand techs or luxuries or resources or money and I don't give it to them), but I will go to war if they culture flip one of my cities, build a city against my borders that actually impedes on my borders and cuts in on them. In the current game I am playing, I also went to war with the Aztec over Uranium (I had just researched it, it was in their borders and not in mine). I actually didn't declare war on them, they had troops in my borders, I told them to leave, and they declared war on me. But it was an utterly convenient war, because I am much more powerful than they are, and I had my excuse to roll through their cities and get my uranium deposit. Most of the time, tho, I won't go to war for resources, I will just try to trade for it.
Kinda off topic, but still related, the best way that a war I was involved in got started, was, I was massing my troops outside the borders of a Sumerian city that was built on the coast of my area of the continent, and I wanted it (along with control of the 4 - 5 city island mentioned earlier, which Sumeria also controlled at the time). As I massed my armies outside their city, and at the same time I noticed Zulu troops crossing my borders from Aztec. I knew they'd start a war if I asked them to leave, and I didn't want a war with them cuz I was getting ready for one against Sumeria, but I guess Zulu really wanted it with me (dunno why, I was much stronger), and they signed an MPP with Sumeria. Me, being the manipulator I am (

) went to the Incans (most powerful nation in my game) and got trade embargos against Zulu and Sumeria, and got an MPP of my own with the Aztec. Well, right on cue, the Zulu declared war on me (no demands, just war), which got the Aztecs to declare on Zulu, which got Sumeria to declare on Aztec, which gave me my excuse to invade Sumeria
