They've previewed the themesongs for Ryu, Ken, Nash, Vega/Bison, and the Forgotten Waterfall stage last July, and just this past Tuesday, they've also put out samples for Balrog/Vega, Birdie, Cammy, Chun-li, Karin, Rainbow Mika, Necalli and Rashid.
Click on a character (or the screenshot below) to listen to an audio sample.
But of course, it would be more awesome to hear the full versions of these BGMs, so let's wait until February 16, 2016, the release date of SFV for the PlayStation 4 and the PC.