I think a very good, extremely lightweight system is the one used in the Over the Edge game, which came out way back in 1992. The game as sold, was mostly setting material, which you can ignore safely if you're not playing in that universe. The entirety of the mechanical part can be given in about three paragraphs, as seen here:http://en.wikipedia.org/wiki/Over_the_Edge_%28game%29
There's a very clear one-page handout of all the rules you need here:http://www.atlas-games.com/pdf_storage/OTERuleBriefs.pdf
(also look at other links on http://www.atlas-games.com
for other support materials, such as a character sheet).
Honestly I think that there's a tendency to overuse relatively heavy systems like D&D for forum games that really don't need that level of complexity. The bare bones of what you need, most times, are:
1) Some way to tell what individual PCs are good and bad at, and to compare them to each other when necessary.
2) Some way to determine if character actions succeed or fail.
3) Not much else.
And as HairyHeretic mentioned, there are literally hundreds of systems out there. If this one doesn't fit the bill, there are many others to choose from. Here's a page that lists over 500 of them, all available for free.http://www.darkshire.net/jhkim/rpg/freerpgs/