Well that's what I get for being cocky. Several civs kept trying to plant a city in this corner of my territory that I hadn't managed to colonize yet so I destroyed their city each time. After the last time, the next thing I know everyone was at war with me. I had a + 10 on "You declared war on my friend" with everyone of them. I was powerful, but not powerful enough to fight 6 civs at once. Especially with War Weariness starting to kick in. I guess I better keep a eye on my diplomacy in the future.