Dr_Worm: The only real benefit is being able to talk to your Steam friends in-game, but many games don't work with the Steam overlay (any DOSbox game, for example).
That's wrong for a start. DOSBox games work fine with the Steam overlay, just as long as you use OpenGL output (configurable from the config app or from the .conf file). There are numerous games on Steam that also use DOSBox (Commander Keen, Dark Forces, Wizardry) and use the Steam overlay just fine.
The only things you'll be missing out on in Steam are the achievements, trading cards and cloud saves (assuming that the game supports these three).
Now what is true is that some games - mainly early 90s Windows titles - will not work with the Steam overlay owing to the fact that they use DIrectDraw or Direct3D pre-DX7, but buying the same game from Steam wouldn't remedy that (Jedi Knight, for example).