System for Low Fantasy Campaign

What would be a good system for running a human only or a typical fantasy races/monsters campaign with little to no magic? Something like, Lord of the Rings or Game of Thrones.

Barbarians of Lemuria could work, if you're into Conan-style swords & sorcery. It'd be easy enough to skimp on the magic by tossing out a couple of the careers (like the magician), or at least limiting access to them. Unlike D&D, where removing casters dramatically fucks with the game, it really shouldn't be an issue in BoL.

Burning wheel for something like Game of Thrones.

Harnmaster, if you don't mind amputation rolls.It uses a handful of charts though, so if you're allergic to that, it's not for you. It's nowhere near Rolemaster-levels though.
Other than that, WFRP 1E/2E.

Song of Swords soon, my friend

GURPS with Low-Tech, Martial Arts, Thaumatology: Ritual Path Magic and possibly some cherry-picked stuff from the Dungeon Fantasy line like streamlined play rules/guidelines, monsters, treasure/artifacts, and wilderness exploration.

If you wanted to get 'really' into it, you could also use Lord of the Manor/City Stats/Social Engineering/Boardroom and Curia/Mass Combat to get the most out of the GoT side of things like raising armies, expanding and maintaining your keep, politics and conniving/social maneuvering, raising armies and laying siege to cities, etc.

If you don't like GURPS you could try Burning Wheel for LotR (also crunchy but more narrative), ACKS for GoT (light OSR), or Fate (for either in a more narrative rules-medium flavor). Riddle of Steel, Song of Swords or the like would also do well for the GoT-alike.

Fantasy Craft (if you're a D20-head) or Legend or Mythras would also be pretty decent choices for either.

Isn't it terribly complex for newcomers though? There's been a general on Veeky Forums since forever but can you give a summary of the mechanics, classes and gameplay?

GURPS is the correct answer.

Gurps.
Also works for high fantasy too.

>Classes
None

>Mechanics
Have a dicepool that renews every round, allocate dice from it to attack and defence maneuvers (like The Riddle of Steel).

>Gameplay
Very deadly combat. Also groinstabbing.