I'm a relative newbie to Traveller. I played CT for the first time back in 2006, picked up the LBBs and then the Mongoose edition when it came out. Prior to 2006, my sporadic SF gaming was done with Star Frontiers, Gamma World, and Fading Suns.

My biggest issue with Traveller -- which isn't really saying much -- is that I'm not a Hard SF guy, I'm a space opera and science-fantasy guy (and a lazy one at that), and it seems that some of Trav's subsystems are geared towards the folks who want more Science in their games. I really like the 2d6 vs. DM mechanic and the character creation system, but I handwave or houserule a lot of the extra-fiddly bits like trading and space combat.

My favorite published Traveller setting is New Era 1248. Things are a bit more stable than in TNE but the post-apocalyptic vibe lingers. There are some established and growing power blocs and looming struggles, but there's still plenty of rebuilding, exploring, and re-exploring to do. The setting seems wide open, and the future is blessedly free from 30+ years of canon...