[PvK]

First, I loathe the "4X" label, and games that really are limited to the simple explore, expand, exploit, exterminate model.

Expand & exploit are often done in simplistic fake-o ways.
Exterminate is just wrong. Agro-civilized humans' 4X attitude is liable to kill ourselves off before we even get to the explore stage.

I like games that create an interesting game universe where many different things are going on and interrelating, that you can interact with in creative and interesting ways.

I also like interesting tactical situations and the opportunity they create to use cleverness to effect (even if I can only guide the tactical AI in advance). At the very least, I want a "4X" game to provide context for interesting tactical engagements.