Yeah, Darius is always there for me too. But I like him, he's always pretty cool. And he has an awesome beard. And a pretty good AI, it seems.
Ramkhamkheng is always there too, but always on the other continent eating up city-states.
Lately, I always seem to be next to America though. That's the one civ I always hate seeing, because they just feel so egregiously out of place at 4000BC (plenty of other civs are out of place, but to nowhere near such an obvious extent). And it never seems to be on the other continent or anything, but right near me trying to start wars and being rubbish at it then sitting around being broodingly passive-aggressive until I'm forced to go and put him out of his misery.
But yeah I really love being surrounded by proper ancient civs. I should specify in my next game that it must include Persia, Babylon, Egypt, Greece, Rome, China, India....