Well I can recomend a few I have played in my time...
On the 360...
Castle Crashers - It's pretty much Golden Axe but in flash. You have a leveling system that gives you points to spend on stats (Power, Defence, Speed and Magic), you can adopt pets who help/hinder you (The bipolar bear is funny as it attacks absolutley EVERYTHING on screen... even you.) and a shedload of weapons with 4 player co-op both on and offline. Also available on PS3
Dungeon Fighter Live - Has a good Anime feel to it with it's visuals and plays similar to the above game, but the class system is limited to 3 types. The sheer amount of abilities and attacks each character has is great though. This is however a dumbed down port of the free to play Dungeon Fighter Online... but is not available in the UK.
On PC...
Phantasy Star Online Blue Burst - An excellent dungeon crawler game where you can take missions with up to 3 friends/random companions. The official servers closed a long time ago however and is now played on a private server for free without subscription that runs the Dreamcast, Gamecube and PC versions. The site also allows you to download the game too, but it's kinda legally grey as it is made by Sega but the game is discontinued and no longer available in material form for the PC.
I have been meaning to get back on DC Universe Online too, it looks pretty good and is also free to play though with a lot of the features cut until you actually subscribe... the good thing about the subscription though is that the expansions are included as part of it.