Also by Anne McCaffrey is The Dragonriders of Pern, which seems like fantasy at first blush but is really science fiction set on an alien planet with genetically-engineered dragons. It's a long series that's told out of chronological order and has been taken over by her son, I think, following her passing.
There are the classic universes of decades past. There's Larry Niven's Known Space series, best known for the Ringworld novels. Hugo mentioned Asimov's Foundation series, which is part of a larger Asimov future history also including his Robot and Galactic Empire series (which started out separately but were tied together into a larger whole in his later works).
If you want stuff from Star Trek authors, there's David Gerrold's War Against the Chtorr series, which has been unfinished for a couple of decades now, but Gerrold says he's getting close to completing it at last. Of course, he's done plenty of other standalone books, but you asked about universes. He's done a couple of others, like his Star Wolf series and the Dingilliad, a trilogy in the vein of Robert A. Heinlein's juvenile novels. Let's see, Trek novelist A.C. Crispin and others did a series called Starbridge, IIRC, about a sort of interspecies space academy -- kind of Trek-like in spirit, but with more diverse aliens.
