While I've found plenty of hotels in the Carribbean, Mexico, Greece, and the French Polynesian Islands that have private plunge pools, there are only a few that I know of in the US, at least that are less than $800/night:

Amangiri
Cosmopolitan (Las Vegas) - doesn't really count since they look to be about 4 square feet
JW Marriott Scottsdale Camelbak
Phoenician
Belamere Suites

Are there any others that you've stayed at or heard of?