I didn't play too many games as a kid (my parents didn't really care for them, so we never had any consoles and only a couple PC games). But one game that does stand out was Star Trek: Starfleet Academy... you became a cadet at the academy and flew a bunch of simulated missions in classic Star Trek ships. Your instructors were the crew of the original Enterprise (played by the original actors), and there were a lot of between-mission scenes where you could make choices that would affect the rest of the game. It was a pretty long game, and I really enjoyed it!
Gamer Challenge #1 - Starfleet Academy
Interplay would go on to create the original Fallout series, and later on Baldur's Gate and the Descent series.