California by a long way - total of 24. This site lists them all:
http://www.whitepages.com/maps/CAWhich state has the most area codes?
California is number 1 with 27 area codes. I double checked the count because kamaole3's count of 24 would have tied Cali with 2nd place Texas. I thought the following site was a little easier in spotting the repeats:
Report AbuseWhich state has the most area codes?
I'm guessing California. Big area and heavily populated. Don't know the codes.