To clear up any confusion: M@nticore was referring (I think) to the unworn ridge at the edge of the brake disc? If this is more than a millimetre deep, it's time to change the discs.
Sometimes the minimum thickness is engraved around the edge of the disc (of course, with salt on the roads that is probably long-gone).
The minimum thickness of 9mm that (CZ)enda quoted is correct, but when new they are 10mm thick - so only 1mm allowed for wear.
In my opinion, the overall condition of the discs is more important than just the thickness. Be careful to look for heavy rust around the narrow part in the centre (where the disc joins the flange - sometimes they can shear!), deep grooves (do they catch a fingernail?), warping (juddering when braking), or overheating (bluish colour). Cracks are less common but still possible if the discs were overheated.
If smooth and shiny I would treat 8mm as a minimum, but then again I saw a FIAT Tipo with the discs down to just 5mm and the brakes were still working OK. It is risky having the discs that thin, as they could warp if they overheat.
When I fit new discs, I treat the centre and the edge to a coat of zinc-rich primer (it was called CRC Cold-Galv or something similar).
As for the pad thickness, at least 2mm is necessary and I like to have about 4mm or so, because with less than this the brakes will overheat and fade very easily. The right choice of pad can make a big difference to the braking performance - please don't just buy the cheapest you can find
Go for a name brand like Ferodo or Mintex.
-Alex