I used to use Sonique (RIP) and Winamp with the MAD/Otachan ASIO plugins and the ASIO4All drivers since the early part of the decade. I've begrudgingly been using iTunes just because it has collateral features, like the music store for doing some searches etc. Now I'm trying out foobar2k. The UI is very plain (yet functional).
Also for music streaming sites, I'm using Pandora, Sky.fm/di.fm, and a little of sky.fm, but didn't really stick.
Any other apps/sites that people can recommend?