First splatbook you begged your DM to approve.
The first book I've ever asked and to be approved would have been the Expanded Psionics Handbook. I love the concept of Psionics personally, and I really wanted to play a character out of that. Probably the next two books I discussed with my Dm were the Complete Psionics book for a prestige class, and the Draconomicon so I could try to have a Dragon companion. All in all that was all for one character only, and it turned out to be an great character to play.