If you haven't already done so, install the BUG (BtS Unaltered Gameplay) mod. It doesn't alter any of the rules of the game or create any new units, but it
does give you all sorts of helpful notices while you're playing. Two of those notices appear on the civ list that lives in the lower-right corner.
One notice is a power number, which is simply a numerical comparison of your (military) power rating versus each of your opponents. When you see those numbers dropping below 1, watch out! Military weakness invites sneak attacks, especially from certain AI leaders. (Genghis, I'm looking at you!) When your military is lagging behind your neighbors, start recruiting some troops ASAP in order to avoid war.
The other notice is a red fist that tells you when an AI leader has gone into WHEOOHRN (We Have Enough On Our Hands Right Now) mode. When you see that red fist, it means someone is about to go to war. You might be the target, or you might not be. But
someone is going to feel the pain. Check your power rating (see the first notice) and check your diplomacy situation!
If you don't like mods, you can get all of this information from the vanilla game. Just check the power graph on a regular basis. Talk to all of the AI leaders to see if they're in WHEOOHRN mode. It's a pain in the fundament, but it'll keep you out of war.
Or just install the BUG mod. Now that I'm used to it, I wouldn't play Civ without it.