Tabletop role-playing games (RPGs) are a particular (and arguably, the original) form of role-playing game.
Participants play characters which consist of different numerical attributes describing their abilities, skills and various other parts of their personality and guide them through a world described by the system's setting and the system's rules, which form the game mechanics. One person is responsible for telling the story, presenting plotlines to the characters and who interacts there are some diceless system, too.
Game systems usually consist of a set of rules and a description of the setting, i.e. of the game world and the different peoples. In most RPGs, Player Charcters (PCs) can be of different races (more properly, species, although most games use the term 'race'), depending on the setting Elves, Humans, Dwarfs or all sorts of aliens) and of different Character Classes (in fantasy settings these might be Barbarians, Druids, rogues etc. while in Science Fiction settings they might be Space Craft Pilots, Street Samurai or Hackers, etc.).
Apart from commercial systems there are countless homemade systems written by gamers for themselves and their friends.
Games
Fantasy settings
Science Fiction settings
Contemporary settings
Historical/Period settings
Steam Punk/Steam Fantasy
Wild West settings
Pulp adventure settings
Superhero settings
Time travel settings
Miscellaneous
Generic games with multiple settings
Magazines
Old magazines
Comics
Fanzines
Major Websites
Companies