Games like Mafia 2 or L.A. Noire

Godfather 1 and 2, Mafia 1 :D

It might be this that you're looking for.
Or try Indigo Prophecy/Farenheit even though I don't really recommend that game

edit: I have no idea what games can be similar to Mafia, but 2 games above are murder solving games that you might be interested in

I really really liked the two games both LA Noire and Mafia 2, the only thing wrong is that Mafia 2 has a short history.

Sleeping dogs, better than mafia and la noire.

i wish for a mafia 3, mafia 2 was so good :)

I think you're looking for noir games...honestly the only other noir games I know is Godfather (I have played 1, quite enjoyable it was)

Damn, I have never thought about the lack of noir games on the market even though they can be fucking awesome...I think I will go rewatch Memento and Sin City now.

Fortix.

If you're looking for the same theme, try out Omerta - City of Gangsters, or Face Noir.

If you're looking for similar gameplay, then try out Saint's Row, or Sleeping Dog.

You might find your fill in Batman: Arkham Asylum/City too, as they are somewhat Noir 3rd person games.

These are usually referred to as "Open World" games.\

So, others like this include GTA3 and newer, the Saint's Row games, Sleeping Dogs, and so on.