Perhaps some people use recommendations like those at Amazon, but I think generally most people avoid them because (at least at present) the signal to noise ratio is ridiculously bad.
It's based on the Music Genome Project. For over 8 years, they've been having highly trained musicologists listen to each song individually, then manually categorize them on ~400 attributes (e.g. is it syncopated? major or minor key? does it have vocal harmonies? etc). Pandora uses this data to find similar songs to the ones you like.
You'd think it wouldn't scale but Pandora seems to be doing it.
"The Music Genome Project's database is built using a methodology that includes the use of precisely defined terminology, a consistent frame of reference, redundant analysis, and ongoing quality control to ensure that data integrity remains reliably high. Pandora does not use machine-listening or other forms of automated data extraction." http://www.pandora.com/about/mgp