If you're looking for a real-time strategy game set in space, get Sins of a Solar Empire.  If you like turn-based strategy, you can't get much better than Galacitic Civilizations 2! 

It's not exactly new but Space Empires V is pretty detailed, but other than that off the top of my head i can't think of any "complex" sci-fi strategy games, most of them try hard to avoid being complicated. I suppose you could go for MoO3 but, well the less said about that the better, and again old.

I aggree 2 of the best games for turn based and real time.

Sins might seem simple but there is a lot more to it than you think specially online.

I would though suggest getting both expansions for GalCiv 2 and the current expansion for Sins.

While I love Sins of a Solar Empire, I find it a bit more on the RTS side.  It is quite deep for an RTS, but it has limited empire building components, so while you CAN play epic sized, epic length maps, I find it repetive because you run out of technology options and planetary development options rather quickly.

Here are my recommendations for very deep space strategy take over the galaxy games:

Galactic Civilzations 2 with all the expansions is probably your best choice.
very deep traditional turn based game with strong empire building components -- also good for artistically designing ships

Space Empires IV if you don't care about graphics
Lots of detail, ship design, empire building, technologies, etc.
I can't speak for Space Empires V, it was full of bugs, but they might all be fixed now)

Sword of the Stars with expansions
very good if you like rich ship design and the tactical RTS ship battles embedded in a turn based strategy game (kinda like Total War series has RTS battles inside of turn based)
not as good if you like sim empire building, but you can have satisfying epic length games where you are continuing to develop your technology and strategies -- it isn't the same fight over and over because there are hundreds of ways to design your ships.

Master of Orion 2 and look for the unoffical 1.40 patch
classic awesome game that holds its own today, but graphics are dated and you might not be able to get it to run on your computer.  Assuming you can find a copy of it.  Avoid MOO3

If you have Civ IV with Expansions, you could try the Final Frontier mod which comes with Beyond the Sword, which isn't too bad.  There is also a user generated conversion mod based on the Star Trek Universe which I hear is impressive, but I haven't tried it yet.  Look for this stuff at civfanatics.com.

If you are a Star Trek enthusiast, you could try and find a copy of Birth of the Federation and some of the user rebalancing mods for it.  Not as old as MOO2, but old enough to be hard to find, hard to run, and it is also buggy, so you probably want to just forget that I mentioned it. 

Many of the above suggestions are good, but I'll add one more. Have you tried Homeworld (theres Homeworld 1, 2, and Homeworld: Cataclysm)? I'd recommend starting with the first game, but I never actually thought the story was that great so you can take your pick. They are RTS titles. I don't know if they meet your requirement of "complex," but I certainly found them challenging and fun. They are relatively old so they should be pretty darn inexpensive if you find them.

Oh and Phalnax811 suggestion of X3:Terran Conflict isn't a strategy game (though it is complex and you need to use your head to really play it). It is, however, one of the best sand-box Sci-Fi games I've ever played and you should definitly check it out to see if it's your sort of game.

BOTF was an amazing game. Sadly unbalanced, with some very annoying problems (who builds a colony with lvl 1 buildings when you've maxed research and have lvl 9 everywhere else?), it was nevertheless an amazingly fun game. There's a fan created sequel being worked on with an open beta, though I dont remember the link off the top of my head.

Yeah, I tried the Ultimate Dominion mod last year when I was kind of bored -- it was a pretty awesome mod!  I also use XP for backwards compatibility, and didn't have problems, but I saw a lot of threads from people who do.  The pace of the game is a little slow for me, but overall it is a pretty good epic strategy game, especially for folks who like Trek.

Yeah, I mentioned it is not complex as an empire builder, but the ship technology and design aspects combined with the unique racial hulls and engine types make for a lot of radically different ship designs.  The ships have real advantages and disadvantages in the RTS combat part of the game.

Plus you add some of the unique encounters, and it has its own epic flavor.  There is also a randomized tech tree every game for each race, so you often have to pick new strategies when you are missing a favorite technology.

Not so good for people who like to manage building advanced research stations, special manufacturing and civic buildings on their worlds.  Pretty nice for folks who like to design ships and then get to control them in RTS combat.

www.homeworld2complex.com

About as complex as you could ask for in a space RTS.

Star Wars Rebellion is pretty good.  That is, if you can find it.......

Indeed. Though I only have Reunion.

I have to agree with Martok. SEIV is about most detailed one on the market today. For an across the board title you should given GC2 a try. It is really a jem.

Thanks, will do.

Another old space 4x game you can add to the list might be Stars!

I haven't looked so I'm not sure how easy/hard it would be to find.