Fudge is a popular system of mechanics: http://www.fudgefactor.org/rules/
Here's the freely available bits of the D20 system, though I'd be lying if I said I thought they're in the running for "best" - most popular, at least. http://www.wizards.com/default.asp?x=d20/article/20040121a
For more anime-flavored / cinematic games, the Tri-Stat system (originally published in Big Eyes, Small Mouth) is available for free here: http://www.guardiansorder.com/pdfs/goo_TriStatdX.pdf (Warning, PDF Link!)
I was pretty enamored of The Window in college, but I haven't looked at it in years - but, hey, it uses that D30 that you, as a hardcore geek, certainly must have lying around the house: http://www.mimgames.com/window/
Hope this helps! Most of the things here are systems, of course - people are generally unwilling to make all the creative bits of their world free, but they're quite happy to share how they use the dice and paper so you can put the creative bits of your favorite world onto their rules.
Happy gaming!