... you'll probably know some of them.
Star Control II
If you don't know it, you're missing one of the most exciting, memorable and funny "explore the galaxy, loot planets, talk to (and shoot) all kinds of aliens" games out there.
Starflight I and II
Ah, the classics. They probably started the whole genre. Probably not worth playing nowadays, but well worth remembering.
Star Command
This one's a bit obscure. It was made by the now-defunct company SSI and focused on space combat and tactical combat (you could even board, and then tow, enemy spaceships if they were the last enemy ship remaining), but you could also do quite a bit of exploration and looting. Leveling up the crew and earning enough money to repeatedly upgrade and change your spaceship was a big part of the game, too.