I just visited the Rockabilly Hall of Fame to see what is going on in Rockabilly music lately and discovered that they sponsor a webpage with tons of rockabilly songs that you can listen to for free. It's called MP3rockabilly.com. They also have it set up to buy albums online to help support the page. This is a great way to become familiar with the music if you are just getting into the scene, or to explore some older or more obscure tunes.
Here are some suggested tunes to listen to on the page:
Baby, Baby, Baby - Joe Allen & the Alley Cats
Dirty Dishes - Jeani Mack (make sure and see the video too!)
Move it on Over - Rose Maddox
Rock the Joint - Bill Haley & the Saddlemen (obviously they recycle their guitar solos)
Stranded in the Jungle - The Cadets
Twenty Flight Rock - Eddie Cochran