The X-ray machine I got a while ago came with a little G-M tube (a Mullard ZP1481). This seems quite a common tube used for demonstration experiments and is still available from the likes of Philip Harris (http://www.philipharris.co.uk/product/Geiger-Muller-Tube-Mullard-ZP1481-B8A49724).
I cooked up a circuit to detect pulses from the tube and indicate them both on a piezo speaker and a white LED. Here's the circuit (click for larger):
I found the tube worked best at around 430V. Pulses from the tube are amplified by Q1 then inverted by Q2 to power the piezo disc and white LED. There's also a BNC output so the pulses can be viewed on a 'scope. A 9V battery can also be used in place of the 12V supply, to avoid any problems with PSU-related noise.
Obligatory photos. I bodged the circuit into a flimsy plastic box that held some business cards - not great, but good enough. The piezo disc is taped to the lid, which acts as a sounding board.
Short video of it in operation. It detects alpha particles nicely (from my Americium-241 source).
For another method of detecting radiation, see my spark radiation detector.