System-wide, there are several names for them. The ones that come at the top of my head are D20 (D&D, all editions, several 'off shoot games, like D20 modern), then there's Dice Pool (WoD, Shadowrun...) Then there's my Iron Monger (A system I developped that's based around a hybrid of a few systems...) now, the beautiful thing with Iron Monger, it would be very easy to implement into a website since it has One System for Everything. But well, its not really complete yet. I've completed the Grid Based RPs for it, but not the "Gridless Ruleset" ... so it wouldn't yet be the best of choices when it comes to sites. Anyways.
We could have a bit of a system built-in into the site. Something open-sourced, and open-creative so people can make what they want out of the rules they have for RPs. There are quite a few systems we could look into, but that would be something of a shiton of work to implement...
Now, generally, its not going to be possible to list all systems available into a list, because that list is evergrowing as we speak. People develop systems, systems get extended, systems get obliterated...
D20(D&D, Pathfinder, countless variants...), WoD (Vampire, Werewolf, Mage, etc...) NWOd (same, but ... revewed rules or something.) Returners' Final Fantasy (Pretty much an abandonned project...) Iron Monger...
So in my opinion, a list of the most common systems (D20, WoD, Other...) and a way to add a line to describe which system exactly it is that we plan to use.