Explore Alterra is a tabletop RPG that eschews a character sheet in favor of cards that measure spells, weapons, armor, talents and items. It is a very straightforward system, and an interesting setting.
GDW’s Classic RPG Traveller from the late 1970s is currently available for free at Drive Through RPG.
Dread is a role playing game that uses an innovative mechanic — a Jenga game — to resolve actions and build tension.
There are both free and paid versions.
Steve Jackson’s GURPS (Generic Universal Role Playing System) is one of the grand old men of the role playing world. The game provides one of the most realistic, detailed gaming systems ever. Because the combat system is so good, I know of many miniature gamers who use it for skirmish games. Steve Jackson games has released a free “lite” version of the rules as a pdf download.
Tombstone is a free RPG set in the wild west. It’s designed to be rules-light, and has quick play character creation to get you started.