Answer:
There are currently (in 2010) 13 temples operating in Utah and 2 under construction.
The temples in Utah are:
St. George
Logan
Manti
Salt Lake
Ogden
Provo
Jordan River (in South Jordan)
Bountiful
Mount Timpanogos (in American Fork)
Vernal
Monticello
Draper
Oquirrh Mountain (In South Jordan)
Those under construction are:
Brigham City
Payson