I've been seeing the term 'Action RPG' or similar used more and more these days describing just about any shooter which is more complex than Doom.
To me an RPG must be a game which give real choice when it comes to your character's development and choice about how to tackle the game itself (and for preference, repercussions based on those choices). Calling games like Bioshock an Action RPG seems like a total misnomer, rather than a FPS/RPG hybrid it seems more like a FPS with a case of the RPG man-flu, its RPGish but it'll get over it in a day or two.
The likes of the original Deus Ex were as close as anything ever got to a proper action RPG, choices you made severely affected how you played the game, there was enough scope in most situations for you to approach a solution in a few ways but it still managed to keep you on track for a pretty fast paced, story oriented game.