Over there, health care in general is super cheap (compared to the USA), and there are plenty of good hospitals/dentists/etc. in Bangkok. I'd bet they're good and cheap in Phuket too. You could probably even pay cash for services like annual dental and vision checkups.

I've signed up with WorldNomads.com for general accident insurance. I've never gotten sick or hurt so I can't personally vouch for the claim process. However, they're recommended by Lonely Planet and a bunch of other notable travel sites. They're worth checking out.

Also you could check out the Lonely Planet message boards too.