Oh boy.
Well, I've played almost every 4x game there is, and Moo1 & 2 holds a special place in my heart.
There are some other good ones that has been released though.
Moo3 - the less said the better. A good example of listening too much to the players, I believe. (We want more of that and that and that and oops it became overloaded with details??)
Sword of the Stars is one of the better successors, but it's also not for everyone. Lighter on micromanagement by a long shot, it's really mostly about building starships and blowing up others' ships, and it's the only one with real time tactical starship battles. Which it does a rather good job of. Planetary bombardment with siege drivers is such fun. 
SOTS2 is in development, which is definitely worth keeping an eye on.
GalCiv 2 - sort of the other evolutionary branch to SOTS. Heavier on the planetary development and details, lighter on the starship combat, without becoming hopelessly cluttered by details. My preference is on seeing huge dreadnaughts pound at each other 'til something gives, but GalCiv is still quite good, and its racial options seem more developed.
Sins of a Solar Empire is not really a successor to Moo, in my opinion; it shares few details. It is a limited 4x game with many RTS elements, or even an RTS with 4x elements, if you prefer. Still, it is a good game in its own right, though.
Hegemony, and even Star Wars - Empire at War could qualify, but both fall short in some way, although both are somewhat interesting games. I remember liking Hegemony, but it wasn't memorable - at least I can't remember much from it. 
The thing is, right now, depending on what you prefer, the options are SOTS *OR* SOASE *OR* GalCiv 2, IMO. They each have strengths that appeal to some 4x players. Neither of those got the balance just right, like Moo did, at least for me, but there are some very good successors.
Still, definitely going to look at Moo4 if it's ever released. Also definitely going to check out SOTS2.
