The music is in the Geico commercial where the two caveman are on their motorcycles is, The Sounds - "Hurt You".

The music in the Geico commercial where the cavemen is on the moving sidewalk at the escalator is "Remind Me" by Royksopp.

And the latest music is a remake of "Somebody's Watching Me" by Mysto & Pizzi which you can download directly from the Geico website.