Honestly, I think Moo3 gets a bad rap, though it does need mods to render it playable. One thing it does really well is let you play the macro-game, not the micro-game.
I'll second this, especially with the "chocolate" mod pack and patches it becomes a really great game. It isnt MOO exactly, but it is a different Macro style gameplay. Feels much more like you are in strategic command of an empire and less like you're an omnesciant micromanager.
Space Empires 3. Because you can cut yourself off from all the other star systems in the galaxy by closing the wormholes between them, then devote 10 years to buildinga fleet of cloaked robot kamikaze ships armed with system destroying sun exploder bombs, then unleash them upon the rest of civilization.
You could do this in SE4 also, I think the "stellar manipulation" features there were even more advanced than in 3, you could build ring and sphere-worlds, destroy and construct planets, asteroids, and nebulae. It was missing the deep-space and asteroid colonization of STARS!, and due to engine limitations I dont think you could even mod it in. They were supposed to fix that in SE5 but I'm not sure how it ended up working out. I only looked at it for a fairly short while.
Like everyone else, I've got a soft spot for SMAC. It wasn't a "4X in Space" as much as it was a sci-fi Civ on another planet -- but I liked the research tree in that it was possible to pursue transcendence without colonizing the stars. I'm a fan of the accelerating technology models (rather than a plateau of stability based on current silicon limits and state models) and I think its a bit crazy that a civilization could be building massive stellar constructions without having transformed into something altogether unrecognizable.
On the other hand, anachronistic space opera is awfully fun to play.