According to the paper linked to by david, recovering overwritten data was possible with floppy disks but near enough impossible with modern hard drives, so the recovery idea is probably best considered a myth.
I'm leaving my original answer as representing the myth.
NOTE: The "myth" is about recovering data that were physically overwritten. Recovering data that were merely deleted (not overwritten) is a different discussion altogether.
To the best of my knowledge:
When you overwrite data on the disk, the old data are lost to normal system tools. (If they weren't, a read would return a mix of the bits belonging to the old and new data, so your data would be corrupt and you would need a new disk.)
But it may be possible to recover overwritten data using special equipment. The reason is the way a bit is recorded on a magnetic platter: A "bit" is a magnetized area on the disk. The area representing a single bit contains a few hundred magnetic "grains", and reading a bit will return a 1 if enough of those individual grains have the correct orientation.
The trick is that writing is never 100% - overwriting might change the magnetic orientation of perhaps 90% of those grains, which is plenty for reliable reading of the new data. But there is some residual magnetism left in the grains that didn't change orientation. This residue can be read if you have the proper equipment for it, so you could get a (somewhat noisy) representation of the old, overwritten data. Combined with statistical analysis, it is often possible to reconstruct a fair amount of the original material.
But this kind of recovery requires specialized hardware, and as Oli mentioned is prohibitively expensive for most individuals.