Aside from the 'big three' (Azimov, Clarke, and Heinlein), some suggestions:
I very much enjoyed the Night's Dawn series (Reality Dysfunction, Neutronium Alchemist, Naked God) by Peter F. Hamilton (although the ending wasn't the greatest, I still enjoyed the series). Others of his are good as well.
Iain M. Banks: anything set in his Culture universe is well worth the time.
David Webber's Honor Harrington books (think Horatio Hornblower in space).
Frederick Pohl's Heechee series.
John Varley's Titan, Demon, and Wizard trilogy.
Larry Niven and Jerry Pournelle (I really liked the Motie books: Mote in God's Eye, Gripping Hand).
If you haven't read Frank Herbert's Dune series, I highly recommend them (as well as his other science fiction).
Dan Simmons' Hyperion series.
Lois McMaster Bujold.
Julian May's saga of Pliocene exile (The Many Colored Land, The Golden Torc, The Non-born King, The Adversary)
*edit* Oh, and I'm a big fan of C.J. Cherryh. If nothing else, check out her Chanur series (Pride of Chanur, Chanur's Venture, The Kif Strike Back, and Chanur's Homecoming).