The first active campaign I know about is the game I'm running myself.
The game is a D&D campaign in the traditional style -- exploring weird underground locales, battling strange monsters, "liberating" treasure. So far we've focussed mostly on dungeon adventures, but of course adventures in towns or in the wilderness are also possible. In terms of the style of the games, I'd say the balance is in favour of action and adventure. Mundane activities like talking to tavern-keeps or blacksmiths are largely hand-waved, so that during the sessions we can focus on talking to wizards and monsters instead :)
Inspirations for the campaign include: sword & sorcery (Conan, Lankhmar), old-school D&D (Gord the Rogue, Castle Greyhawk, Gygaxian AD&D), science-fantasy (Dune, Spelljammer). The tone is explicitly non-heroic -- these characters are not out to save the world, they're treasure hunters and adventurers out to get rich quick.
We're playing using the Labyrinth Lord rules, which are a clone of 1981 D&D -- simple and flexible, allowing imagination & improvisation to take the forefront!
We play every 2 weeks on a Wednesday evening. New players welcome!
I'm also running a game at the BurgCon 20 RPG convention in Berlin, come and join in!