When we went to Phuket in Feb we just picked up a taxi from the airport...dead easy went to taxi desk in airport..just given a voucher which was handed to driver. However we had pre booked accommodation, I gather if you don't and use the taxis to help you search for accommodation they demand a huge commission form the property you finally end up in. Many properties and agencies such as Sawasdee.com recommend you prebook transfers.

Don't know fare for Patong...ours taxi to Nai Thon was 400 baht but the resorts was only 20 minutes drive.

We haven't booked transfers either. Quite frankly I'm fed up of waiting for others. Once in a small bus in Bali and went round the whole of Tuban, Kuta, Legian and all the way up to Seminyak picking up passengers... on the bus over an hour feeling sick with the traffic fumes and our hotel was only 10 mins from the airport Also, nearly missed our plane once because of 2 girls... driver had to crow bar them out the bar and they were drunk as skunks singing inappropriate songs about the local sex industry. Then the driver drove at breakneck speed on the wet slippery road round the hills on two wheels to make up the time and never again... Oh! I could go on but I won't.
I posted the same question on a Thai forum recently to go to Kata which is a bit further than Patong. I'd expect to pay no more than 400 baht.
http://www.travlforum.org/thailand/main.html
Hope this helps.
Cheers Geri

Some rates for limousine transfers...just to give a basic idea of price.

http://phuketdir.com/palbuco/rate.htm

Prices seem to tie in with what we paid to go to Nai Thon and our subsequent land transfer to Krabi. Might be worth checking whether your hotel does free transfers to/from the airport...some do. Ours in Nai Thon did but only found that out after we had done the transfer ourself.