Do you love theater organ? Try the Theater Organ Radio Station. Scroll down to the blue SHOUTcast button toward the bottom of the screen and enjoy.
For "classical" organ music, try the OrganLive site. Click on the NOW PLAYING button on the top of their page and then select one of the player options. You may already have one of them installed on your system. I use WinAmp. I also suggest right-clicking and opening the player in a new window so you can keep the NOW PLAYING window open. That way you can refresh the screen to see and research what's currently playing. Notice that you can research the organ, the organist and in many cases you can see or purchase the CD and even the sheet music of the piece that is currently being played. This is one of my favorite sites. They also take requests and you can read user comments about some of the works.
For everything else, try tunein. You can also get tunein as an app for your phone or tablet.