Some great discussion here -- so many different, successful strategies.
I think I'm in the middle here. I will build my first city on the very first (4000 BC) unless the start point is really bad. Usually, my prayer that the Civ Gods will give me two settlers at first is is answered positively in about 50 percent of the time. Either way, I usually research bronze working and build warrior/settler/phalanx. I try to get to five cities in the shortest amount of time possible, having two of the the first three building Pyramids, Wall O'China and/or Colussus.
One reason I feel I can do this is my fondness for playing large maps. I like having a game spin out over several weeks of limited playing sessions.
Getting to monarchy is a big key, however, for me, and my opening strategy is always oriented towards that. After that, I admit, I have to get to Leo's WS -- my favorite early game wonder.
After that it's just build, explore and trade. I try to hold off on the warfare until way after AD 1000 unless forced into it.
But as this thread shows, there's a lot of ways to go at it. Personally, the ICS sounds interesting, but the OCC takes away the fun part of the game for me -- expansion and conquest.