I include the Diablos, GuildWars, WoW, DungeonSiege etc. in the action-RPG category. I consider Oblivion to be a sort of hybrid.
And yes it's important to me. If it's somewhere between WoW and Oblivion, I'll likely try it. If it's a super-serious RPG w/tons of story/dialogue decisions around every corner, I may not, as I don't have the patience lately for such games.