In phuket this is a really rare thing. Occasionally bars will do a special on a particular drink, but havent seen many happy hours. Just confirms this as a very expensive place in thailand to party.
In Bkk, places like Soi Cowboy alot of the bars have happy hours for 2-3 hours, with some crazy prices (35 Baht), also places like Gulivers in Soi 5 have some good drink specials.
Pattaya have happy hours galore. Many places do 12pm - 8pm happy hour, and even some bars doing a 24 hour happy hour (happy day?)
Prices for beers on said happy hours can be 35-45 baht for a bottle of heinekin
mg:
Personally i think happy hours are a great marketing tool which phuket seems to be above. Pack punters in early on (when it would be dead anyway)... sell drinks cheap or near cost. After happy hour, sure some will leave but some will stay on and drink more. All when otherwise trade would be quiet!
There are a couple of open air bars on beach road just down past macdonalds that usually sell nearly all their cocktails for 100 baht ! plus nice place to sit and look out over the ocean.