Whoa, where to start? Let me begin with a few, interesting but minor examples:
1)
The Pool
As an exhibition of how little is required to make a fully functional roleplaying system, James V. West's "The Pool" is a masterpiece. You can download it for free,
here. Covers making characters and stories through conflict - no tactical or strategic stuff, just characters and what they (try to) do. The rules cover just 3 pages of A4. I have used them for convention scenarios and home games - just add an rpg world description and mix well...
2)
Pendragon
Very tightly focussed on one mythic tale, but a beautiful game for all that. Not tactical or "play to win" style at all; figurines and maps can be colourful and fun but are absolutely not required. Players take the roles of knights in the time of King Arthur; magic use is strictly an NPC thing (except in one edition, and that didn't work out too well). But the knights themselves partake of the magic via their own "virtues" and "vices", that are treated as skills might be in "regular" games. Drive up your Courage and you will gain glory and renown for it - but you may also be compelled to stand there bravely while all around you flee impending doom! The Hag relying on fear magic to beat you, though, may be in for a nasty surprise!
Pendragon is very much written for campaign play; it is almost unique in the rules it has for this. PC knights have one "adventure" per game year, then have a "winter phase" when they train, age, breed and manage their holdings (if they are lucky enough to have any). The full campaign is a game of generations, and you might expect to play your original character's grandson in the final days of Arthur's reign...
3)
Universalis
Now available for ten bucks as a PDF (see
here), Universalis is a GM-less RPG with a difference. It really boils down collaborative world building to its essence; every player gets to define aspects of the game world, to create and build upon characters and even to make up new rules as you go along! The rules mediate just how much any one person can control things via a currency of "coins" that you use up to create or take control of characters, objects, settings and so on. You get new coins by creating "complications" - instances where a character controlled by you tries to do something to a character controlled by another player against their will. "Complications" are resolved using the characters' abilities, allies, players' coins and so on via a dice pool mechanic. The players of the "winners" get to stipulate things about the outcome (with their newly won coins), then the loser gets some coins to modify things, too.
Obviously there is no need for battlemats and such with Universalis; competitive play in the usual sense is not really the point - the competition lies in who gets to drive the story. We have also dabbled with using Universalis as a background-generating engine for "regular" RPGs with some success, but it's a bit early to say how that works out for us for sure.