Fudge

Fudge is a generic role-playing game (or a role playing game that can be used in any genre). Fudge at first was an acronym and stood for "Freeform Universal Donated Gaming Engine" (the "Donated" part was changed to "Do-it-yourself"), but this was dropped. Unlike other generic role-playing games like GURPS or the d20 System, Fudge allows people to build their own specialized RPG.
The Game Master can choose what attributes and skills will be used. These are rated on the following scale: terrible, poor, mediocre, fair, good, great and superb. They also choose Gifts and Faults. The game also uses specialized dice. They have plus, minus and blank sides. These four of these dice are rolled. For every "+", you go up a step higher (ex: fair to good). For every "-", you go a step lower (ex: great to good). Blanks do nothing. You do this for every trait.
The rules of Fudge are customizable so the game can be complex or simple. However, the rules (overall) encourage role-playing over the rules. In fact, the game encourages players to "Just Fudge It", which means focus less on the rules and more on the story.
My source was Wikipedia.

Dungeons & Dragons: The Original Edition

I am going to talk the original edition of Dungeons & Dragons, the first role-playing game ever.

The game was a "fantasy system with medieval European flavor". The players could choose 4 races (humans, dwarf, elf, hobbit [this was changed to "halfing" due to legal reasons]), 3 character classes (fighters, cleric, magic user), 3 alignments (chaotic, lawful, neutral) and a handful of monsters. The game also other concepts that would become standard like magic items, treasure, armor class, subterranean dungeons full of traps and abilities (strength, intelligence, dexterity, etc.). However, the game was difficult (if not impossible) if you never played Chainmail wargame, Outside Survival board game or any table top war game. However, Greyhawk supplement supplied new combat rules that made it easier for new players. This led to an entire industry of role-playing and both offical and unoffical supplements.

My sources were the following Wikipedia pages: "Dungeons & Dragons (1974)"; "Editions of Dungeons & Dragons", section "Edition and version history", sub-section "Dungeons & Dragons"; and "Greyhawk (supplement)".

Toon

Toon: The Cartoon Role Playing Game is a humor role-playing game inspired by Warner Brothers cartoons like Bugs Bunny. In the game, the players take on the roles of cartoons.

While the game does parodies more "serious" role-playing games, the game is playable. First off, the characters (like in many Looney Tunes-style cartoons) don't die. They do have hit points that are removed when the character is injured. However when their hit points reach zero, they are simply temporarily out of the game and will come back later with the points restored. Because of the latter, the game encourages you to "Act Before You Think" and to "Forget Everything You Know" (which means abandon the skills you learned in other role playing games). The game prioritizes having fun over everything else (including the rules). If a player does something that the other players and the "Animator" (the game master) think is funny, then it's allowed and encouraged. The game has 23 skills that are controlled by four main attributes: "muscle" (strength), "zip" (dexterity and speed), "smarts" (intelligence) and "chutzpah" (self-confidence and pushiness). However, there is also "shticks" that are unusual (for cartoon characters) abilities such as invisibility and flight.

My source was Wikipedia.