The trailers and marketing for Hancock all quite clearly identify the film as an action-comedy, stars Will Smith and Jason Batemen further cementing the impression. However, Hancock is vastly different to this, and I'd say for the better.
Personally, I'd label Hancock a very funny action-drama. There is no evil mastermind, no end-of-the-world and a thoroughly un-super hero. Will Smith is, as expected, wonderful in the title role, pre- and post-reformation. Alcoholic, bad-tempered John Hancock is an absolute hoot who is easy to root for despite the bad attitude.
That this is a film about people and not about heroics is clear - from Hancock himself to PR Guru Ray's impressionistic son. The set pieces and action are visually brilliant, but are caused and driven by the very individual characters and situations, rather than any grand scale world-dominating supervillain.
The 'mythology' the film introduces does sit a little uneasily, despite being a nice idea. The twist, although enjoyable, never quite makes total sense. The film's ending is touching, Hancock's arc being nicely played out. Charlize Theron's character is a lot more difficult to understand, but not to the extent of ruining the relationship that exists between them.
Hancock might be better in conception than in execution, but the film is highly enjoyable, very funny and importantly very different. Perhaps Will Smith the comedian has been tempered by Will Smith: Serious Actor, and in Hancock this works absolutely for the better.