While nearly everyone who plays role playing games has heard of Dungeons & Dragons, first released in the mid-1970s, most people haven't heard of Tunnels & Trolls. While miniature gamers in the 70s were moving into role playing with D&D, people who weren't so interested in simulating tactical combat were moving into T&T, created by Ken St. Andre and released just a year after D&D.
What distinguishes T&T from D&D is a focus on resolving conflicts as a team, and not on individual activity during tactical combat. Tunnels & Trolls was the first role playing game to use dice pools for conflict resolution. The basic idea is that both sides in a conflict roll their dice, total the results, and the highest total wins. The loser is damaged based on the difference between the totals, adjusted by armor. This applies whether the conflict is a duel between two characters, or an all out battle between two groups. The losing side can decide where damage goes, so those who can afford to take the damage can take the hit for the team.
One of the best parts about T&T, from an early role playing games perspective, is that it introduced the concept of saving throws. These aren't the saving throws we're used to in old D&D terms, where we have a table that says if a character can resist specific effects, such as poisoning, but a generic saving throw based on one of a character's stats. These saving throws are used for resolving anything that happens outside of combat (although for especially important non-combat scenes, GMs might use the dice pool mechanism from combat with some modifications).
Otherwise, there's little to distinguish T&T from D&D. Character creation was standard, rolling 3d6 for each of Strength, Intelligence, Luck, Constitution, Dexterity, and Charisma. Various house rules might allow you to roll 4d6 and discard the lowest die; basically the same sorts of character generation variations that D&D players created.
The basic character classes in Tunnels & Trolls are the Warrior and the Wizard. The Rogue and the Warrior-Wizard classes are merely combinations of those base two, with differing emphasis on what the classes can do. Wizards had a set of spells they could cast, although T&T allows higher level Wizards to channel more spell energy into lower level spells to either increase the effect or duration of the spell.
Tunnels & Trolls was a great system for dungeon crawling, because you didn't get bogged down in simulating the tactics of every battle. On the other hand, if you liked simulating the tactics of every battle, then T&T definitely wasn't the game for you.
Over the years, various editions of the game have been released. Speed was added as a characteristic, some editions revamped the magic system, etc. The system is up to version 7.0 as of this writing, and still retains the essential qualities that make it attractive over a tactical role playing game.
There are free quick start rules for T&T available over at RPGNow.com, so download them and see what you think.