I've heard that Liverpool offered around £90k p/w and Arsenal and Spurs offered him around £80k p/w - If that's the case, that is not a lot of difference at all with todays wages in football so surely Roy must have done something right.
And those of you spouting about him playing for the money (Don't worry, I've quoted you here. And admittedly, I am not surprised who has said it) Get a grip! Have you not thought it might because he wants regular first team football?
Arsenal - Have Arshavin, Nasri and Rosicky who can play in the 'AMC' role - Cole's preferred position.
Spurs - I doubt he would want to compete with Luca Modric for an attacking midfield position, again first team football isn't anything they could guarantee.
Chelsea - They aren't going to drop Lampard for him are they!
Liverpool - Gerrard, that's about it. He can easily drop into Centre Midfield. So surely it was the attraction of first-team football which made him join.