As I've said earlier I started roleplaying in the 80s with Tunnels and Trolls and then gravitated to AD&D (1e) but my first experience of Sci-Fi roleplaying was as a player in a Traveller campaign.
Although I never owned the LBBs (Little Black Books) or the boxed set I did (and still do) own a copy of Double Adventure 1: Shadows / Annic Nova. At this time White Dwarf was still covering all RPGs and regularly featured scenarios for traveller, a favourite of mine being "The Sable Rose Affair" featured in WD 17.
I loved the hard edge that traveller put on the whole Space Opera genre. It wasn't so much about racing through the galaxy to rescue the princess, it was about dealing with the day to day minutia of staying alive in the cold depths of space and yet trying to eke out a living and possibly making that big score. In other words more "Alien" than "Star Wars".
Believe you me, this was hugely influential to my 11 year old self whose Sci-Fi diet at that time was limited to Doctor Who, the odd episode of Blake's Seven, Battlestar Galactica and re-runs of Lost in Space. Traveller also heavily influenced one of the breakthrough 8-bit computer games Elite by David Braben and Ian Bell which I spent many hours playing on my school's only BBC Micro.
In 1984 GDW released Twilight 2000 which focused on the plight of the survivors of WWIII assembling their rag tag militas to fend of the remnants of the soviet army. This got quite a bit of play at the club I was a member of at the time, but it never fit in with my cold war childhod as I recall most of the scenarios being set in the US.
Towards the end of the decade GDW released Space: 1889 which in hindsight shows how groundbreaking GDW were when they published the first victorian Sci-Fi RPG before cyberpunk had truly emerged never mind steampunk. In recent years I have come to enjoy victorian sci-fi more and more, partly as a refracted, quintisentially English, vision of Empire and partly as a result of my fascination with the aestetic of heavy engineering during the industrial revolution (with brass finials and plenty of scroll work).