I'm 100% certain this works with ATI video cards (i'd assume Nvidia can do it as well). I used to do this all the time, just set the TV up as an extended desktop and drag the video over there. Then in whatever video player you use, go into the options and change the sound output device to whatever the HDMI out from your video card is.
Works great in MPC and VLC, for things like Hulu/Netflix/Youtube I don't know if you can do it with the website based streaming, you may have to use a frontend program like XBMC to be able to fine tune the audio settings.