The paper variety, played these mostly in high school. The former president of the Strategic Gaming Club combined Star Wars and Robotech into one game, that is actually my favorite.
Dungeons & Dragons (2nd or 3rd edition) - The classic medieval fantasy RPG that most people will be familar with. Largely based on Tolkein-style fantasy to the point that they had trouble with the estate and had to replace certain elements with a generic version (like the Halflings were originally Hobbits).
If you imagine a world of sword-swinging, swashbuckling warriors and spell-slinging wizards; that is Dungeons & Dragons.
GURPS (?th edition) - A generic rule-set by which any sort of game can be made. No idea what the current version is but it is still around. We used GURPS in high school for our custom games mixing franchises.
Robotech - Based on Paladium Rifts rules set, it is pen/paper RPG based on the Robotech Anime series. My high school gaming club ran a GURPS version, mixed with Star Wars that I enjoyed. The Rift rules are a little wonky and complex in that there is a large number of values to track but is simple in the sense that the same rules are used for everything. No matter what the content (sci-fi, fantasy, whatever) they didn't rewrite the rules like other game companies. Also the company that created Robotech had a hand in some of the content design for the Rifts-based RPG.
I shall forever miss Grey Snowflake; an AT-AT with arms that my character used.
Star Wars - Never played this but included on this list for the GURPS mixed game we palyed in high school. I have no idea what sort of gameplay the official versions are. Current version uses the FATE rules, I think, and know nothing of it.
Warhammer 40k - In high school the minature combat game of Warhammer 40k was played. Several classmates made a pen/paper version that used the rules from the minature game. A traditional TTRPG is now available, I haven't played though. I have read some books and it is more akin to the White Wolf games than DnD but looks to be easy to play and could be fun.
Starfinder - Haven't played this and it is based on Pathfinder (first version). The Pathfinder series was first develpoed as DnD 3.5 adventure modules and later was its own branded 3.5 DnD RPG because of the Open Gaming License. They have since created their own rule-set released as Pathfinder 2.0 but was not demanded by current players.
While Pathfinder is medieval fantasy, Starfinder is kinda Space Opera like Star Wars or Star Trek. There is some influence from anime and video games like Xenoblade but they haven't included any rules for Mecha or powers other than magic and psychics. It is mostly a fantasy game with a sci-fi coat of paint. Some rule changes like stamina and resolve points are half-baked and best to not play with them (or change them so they work).
White Wolf - The other major rpg used by a lot of people was the White Wolf series og games like Werewolf the Apocolypse or Vampire the Masquerade. The 'World of Darkness' (as the series came to be known) has changed alot over the years and is now a community-based project. I am unaware of any current set of source books or games that use it.