Standalone Geiger counters can be had for $100-$300... or you can Geiger-accessorize your smartphone.
Radiation Watch's Pocket Geiger peripheral offers a sub-$100 -- solution for iOS and Android users.
Note: This detects only X-Rays and Gamma rays -- not Alpha or Beta radiation.
You'll also need their smartphone app: the iOS free Pocket Geiger Counter Lite or $6.99 Pro, or the free Android Pocket Geiger app.
For an even cheaper, although not quite as accurate, radiation-sensing iPhone 4 solution, consider the WikiSensor Dosimeter App (iOS, $0.99). (You'll also need something that can cover the camera to block out visible light -- like an inch of black electrical tape, or your thumb.