The Utah State Archives http://historyresearch.utah.gov/indexes have many good free indexes online, birth, death, court, government, etc… They only have what the counties have given them & not all their holdings are index, but this is a good place to look for people that have lived in Utah.
I just noticed in the 1904-1954 Vital Records & Statistics section, they are starting to put the actual death certificate images online.
One thing I don’t like, I don’t see a way to search just one database. But the search engine they do have is easy to use. All you need to do is enter “Surname” or “Surname, given name” or what I like is “Surname, first letter of given name”.