4x games.
It's difficult for me to remember the four x.
eXplore, eXpand, eXterminate, ...
Oh well.
I'm currently on a Master of Orion 3 kick, but I like Space Empires V (I would if between turn processing didn't take so long.) and X3 Reunion.
I guess I'll talk about Master of Orion 3 for a minute.
In Master of Orion 3 you control a stellar empire whose citizens are one of many possible races. You start on your home planet in a solar system. You can always destroy all other empires to win the game. You can also set options to win either by becoming the head of the stellar council (Orion Senate) or you can collect five mysterious technologies by sending out search parties. An unofficial patch at
http://bhruic.dyndns.org/patcher/ can enable an allied victory - meaning that a group of allies will win when all of their enemies have been destroyed. Great if you play a "peaceful" race.
Gameplay itself is somewhere between Risk and Space Empires V. While there are solar systems, they are abstract locations. You can't actually explore individual systems to find locations.
P.S. I'd also be generous and include EVE Online in my picks. While not strictly a 4x game, when you get involved with group dynamics and location and resource control it can seem a lot like a 4x game, except you play as one of the units.