The basic rules for some D&D editions are free, under Wizards of the Coast's license.
Hypertext d20. This includes material from the Player's Handbook, Dungeon Master's Guide, Monster Manual, Epic Handbook, Psionics Handbook and Unearthed Arcana.
Unearthed Arcana: A complete list of the free Unearthed Arcana content, including class options, feats, spells and more. None of it is fully play-tested, so use with caution.
A modern-world RPG which shares its basic mechanics with D&D 3.5, published by Wizards of the Coast. d20 Modern, by Wizards of the Coast.
Is D&D not gritty enough for you? Feel like D&D 4 and 5 are too streamlined? Want a fun, well-organized game that has a rule for everything? Pathfinder, published by Paizo, is an updated D&D game with a huge amount of additional free material.
Play as a superhero! This is a fun and flexible system, allowing you to create pretty much any hero you can imagine. Mutants and Masterminds 3rd Edition
Ars Magica, a system with an extremely complex and flexible magic system, where almost everyone plays a mage. They've released their 4th edition rules to the public domain.
A classless, genre-agnostic system in which you can build your character however you want. Instead of picking class levels, you choose feats to define your character. It bears some resemblance to Mutants and Masterminds. Open Legend RPG
I've been building up a nice collection of one-shot games. These systems can be picked up quickly, even by people who aren't familiar with tabletop roleplaying, and they're a lot of fun.
My favorite one-shot game comes with pre-generated characters, simple rules, a unique setting, and an engaging storyline. It takes place in a steampunk science-fiction world where planets float in a solar-system sized sphere of breathable air. Unlike in most RPGs, the players define the world and create NPCs. The GM's job is to ask leading questions and create conflict. Lady Blackbird
John is incompetent and insane. You are a voice in John's head, bidding for control and trying to get him to do what they want. This is a silly, competitive RPG, and takes about an hour to play.Everyone is John.Character Sheet.
A very simple RPG with just one stat - bubblegum. You start with eight sticks of gum. To do something mundane, you have to roll lower than your bubblegum on a ten sided die. To do something “kick-ass,” you have to roll higher. This game can be fun for any group of people, even a mix of adults and small children. I've played games with a five-year-old, with a group of experienced role-players, and with a dozen people at once. The game usually takes less than an hour. All Outta Bubblegumplugin-autotooltip__default plugin-autotooltip_bigAll Outta Bubblegum
This game is copyright 2001, Michael “Epoch” Sullivan and Jeffrey Grant. If you want to repost it or whatever, drop me an email.
Characters in All Outta Bubblegum have one stat -- Bubblegum. It's technically a number which varies from 0 through 8, though the designers highly, highly recommend that you don't do anything so banal as write down a number, and, instead, pass out actual sticks of bubblegum to the players. This will also help when you play All Outta Bubblegum dru…
Simple mechanics and character building get you going quickly in this science-fiction RPG with the light-hearted adventuring feel of original Star Trek. Roll up a scenario, choose a few character traits, and you're ready to go. Lasers and Feelings
A very silly game, best described by the game's own tagline: “It’s Honeycon 2017. You are going to undertake the greatest heist the world has ever seen. Two Things – One: You have a complex plan that requires precise timing. Two: You are a GODDAMN BEAR.” Honey Heist
The king of one-shots, Fiasco is a game where you create a Coen-brothers style movie. In case you're not familiar with the type, things tend to go from bad to worse, and your goal could be to make your character's life as horrible as possible. It's played in one of many “playsets,” which are guidelines as to the setting and relationships your characters have. The game set-up is great. You go around in a circle selecting relationships, locations and objects that define what kind of story you're going to create. Fiasco claims that it takes around 45 minutes per player. In my experience, a four-player game takes 3-4 hours. The PDF only costs $12. It's absolutely worth it. Fiasco.