If you do a little reading about MP3 and how lossy compression works you'll soon come across a warning to avoid recompressing your files. In general, this is a good idea, since even if you have a super-high-bit rate file, a little is lost just in doing the math to convert between the time domain (the wave file) and the frequency domain (the mp3 file).

But there are exceptions and they are significant. First, recompressing a file once isn't generally a problem with a file that is encoded at 160 kbits or above. Recompressing twice probably isn't a problem either. Recompressing 100 times is bad.

The Sony Minidisc makes use of the fact that recompressing once isn't bad - every time you put an mp3 file onto the Minidisc it is converted into Sony's proprietary Atrac format.

So there you have a product that requires recompression.

Recompressing, of course, is worse at lower bit rates, because more information is thrown away each time. You might think that once the information is thrown away the first time, there would be enough bits to recompress without loss, but unfortunaely due to the way it all works, subtle problems with alignment and the math of it cause further loss. On the other hand, if you have tons of bits, then very little is thrown away each time.