Limiting myself to the Traveller experience, and removing "the usual suspects" (Anderson's Flandry and Falkayn, Norton's Solar Queen, and Dune), I present a few books in the spirit of "you should read these if you are a Traveller player"...
Brian Daley: The Adventures of Hobart Floyt and Alacrity Fitzhugh
(trilogy consisting of "Requiem for a Ruler of Worlds", "Jinx on a Terran Inheritance", and "Fall of the White Ship Avatar")
Larry Niven's tales of Beowulf Shaeffer, as well as his other Known Space stories. Ringworld is actually lower on this list than you might think.
Charles Sheffield's - The McAndrew Chronicles
Anne McCaffery's Dinosaur Planet cycle (Dinosaur Planet, DP Survivors, Sasinak, and The Planet Pirates). Despite the anti-meat thing (which I had no problem taking as a cultural base instead of a RW "message"), these have all the fixins a Traveller tale should.
Poul Anderson's "Tales of the Flying Mountains".
H. Beam Piper - pretty much everything. Start with Space Viking, Cosmic Computer, Four Day Planet, and the collections "Federation" and "Empire".
Michael McCollum's "Antares" books.
John Kooistra's "Dykstra's War"