GURPS

I've decided to list the established tabletop RPG systems in the order I was introduced to them. I met  group who used the Generic Universal Role Play System (GURPS) in my first year of college. This was designed to be modified to fit any setting the group needed, and many fans had made expansion books to cover what the writers missed. It uses an odd system of dice rolling based around three 6-sided dice, rather than the 7-die set that Dungeons and Dragons made so iconic. All skills and abilities were purchased from the same point pool, and could be upgraded to have a better chance of working or a stronger effect. You truly could make characters of any strength, human to superhuman to god. Many stats were given for hundreds of weapons, armor and vehicle ranging from past to future.

As far as story telling was concerned, that was up to the group playing. Resources for settings and monsters were available, but most of the plot is left to the user.