I can only talk about what i think a DM should play like (so i'm not speaking for everyone here).
Basically when i think of a DM, i think the obvious, Keane, Viera, Gattusso, Makalele, Davids etc, someone who can control the central area, hassle the opposition into making mistakes, ultimately making them lose the ball, someone who can cover the defence AND play the ball easily to the more attacking line, but essentially someone that can WIN the ball.
Hi EZ - I think a lot of people think of DM like that - but Veloso didn't look that type of player
Carrick fulfills some of the classic criteria but not others
etc etc