I have the oldest SR game on the Weave, DocWagon Seattle First ResponseTM, though it's currently suffering a little from Players Who Have Lives.

Also, an M&M2e game: Maze Beset.

One of the few Warrior, Rogue, & Mage games: Pentingham. This one isn't 'long-running' yet, but I have much optimism for its long term survival.

A Hunter: the Vigil game (sort of), as well: Long Cold Winter.

I also accept Readers into my other game, Evash, which is D&D3.5.

Oh nice thread solved my query too of not being able to find current games being held.