This game literally invented the genre of the RPG. Invented in the seventies by Gary Gygax and Dave Arneson using variations on the rules from the medieval battle game "Chainmail", this game still gets play in justabout every edition yet published.
If Dungeons and Dragons is the Superman of tabletop RPGs, then Vampire is its Hellboy. Released in the nineties by White Wolf Publishing, this game exemplified dark games, and the horror RPG genre wouldn't be the same without it. Fun fact: White Wolf actually sued the makers of the "Underworld" films, because the vampires and werewolves they depict
Created by Steve Jackson Games in 1986, The Generic Universal Roleplaying System was developed with the express purpose of being able to play literally any kind of character, from gunslingers to wizards to, no joke, sentient muffins! GURPS optional rules for any kind of game, and may be one of the most flexible tabletop RPGs ever published.
Probably the most famous Tabletop RPG, this game literally created the genre in 1974. While it's had a sometimes-troubled history, it's still going strong with its 5th edition, and every edition brought new innovations over the last.
While not the first in horror RPG's, the original World of Darkness is still one of the best. With its preference for story over gameplay, its modern, close-to-life setting, and its rich variety of player options, it's no wonder the original is still in print after 20 years.