GCR decoding on the fly
linusakesson.net
linusakesson.net
The rest of his site is very interesting too - I think some of his other articles have made it onto HN before. I like that he has a series of articles on obfuscated programming:
http://www.linusakesson.net/programming/obfuscation.php
...and below that, another series titled "sane programming":
http://www.linusakesson.net/programming/index.php
His demos are worth watching too.
I don't know of other applications but there has been a Mandelbrot program that used the processor in the floppy as a co-processor.
The C64 has a 6510 processor and the 1541 floppy has a 6502. As far as I remember the only difference are 4 additional IO ports that the 6510 has and that the C64 uses for (memory) bank switching. So for computational purposes the processors are identical.
I seem to remember the 1541 can work with a 6510 too. And the C64 might possibly work with a 6502 too as long as you hardwire the right pins to +5 or ground to get the default memory banks (but the tape drive will be inaccessible).
The 1541 also contains two IO chips - the 6522 VIA that are almost compatible with the 6526 CIA chips in the C64 to the extent that you can "repair" a C64 by pulling the IO chips from the disk drive. I did that as a temporary measure once or twice. They are pin compatible, but the 6522 lacks the real time clock of the 6526, but pretty much no software ever uses the realtime clock (the 6522 have timers instead).
The 1541 really is a pretty complete computer. A lot of the early Commodore designs (and others) really foreshadow modern designs where everything has steadily moved to more CPUs again, unlike typical early PCs that burdened the main CPU too much (one of the reasons - in addition to the OS - that the Amigas felt so responsive even when compared against PCs with faster CPUs).
A few years before it came on the market, people would've paid good money for a device like that to use it as a computer rather than a disk drive...