The thinnest ATX case is probably The Thermaltat Core G3, but that needs an SFX PSU and its thermaltat so i wouldnt get it anyway.
After that it would be cheap cases, as they are smaller to save cost and dont have the depth behind the motherboard, something like the Bitfenix Nova
My basket at Overclockers UK:
- 1 x Bitfenix Nova Midi Tower Case - Black= £32.99