With examples from X-Files and Stargate SG-1
There seems to be a lot of confusion on which word to use, and for good reason. Both words come from the same root - the Latin discus and are not only pronounced the same, they both can be used to describe the same thing.
For instance, according to Dictionary.com, disc is defined as "a phonographic record," while disk is defined as "any thin, flat, circular plate or object."
But despite all this, there is a difference between the two words. Dictionary.com also describes disk as, "any of several types of [computer] media consisting of thin, round plates of plastic or metal, used for external storage: magnetic disk; floppy disk; optical disk."
Discs and disks in the computer world
Apple partially agrees with the above definitions according to this very informative article. They contend that a disc refers to any optical or removable storage of computer information, while a disk stores this information on magnetic media, like a floppy disk or hard drive.
"We can prevent the virus from writing to our hard disk array," Sam told the General. "But there's no guarantee that the mainframe hasn't been compromised."
Mulder pulled the disc out of the CD compartment and held it up to show Scully. "This may be our greatest find, or our downfall." He brought the disc up to take a closer look at it. "Ten to one we're looking for another job tomorrow."
The above article also offers a mnemonic device to remember which one to use: "disc ends in a 'c'—if you cup your hand in a 'c' shape, it’s the perfect grip for holding an optical disc. On the other hand, disk ends in a 'k,' which is the periodic symbol for the element Potassium, which is in the same period as Iron (Fe), which is highly magnetic! See? Easy!"
Medterms.com lists the various uses for these two words on their website. But it appears that both words can still be used interchangeably. While the intervertebral disk is defined as "[a] pad of cartilage between two vertebrae that acts as a shock absorber," the site also lists the definition of disc as "[s]hortened terminology for an intervertebral disc, a disk-shaped piece of specialized tissue that separates the bones of the spinal column."
Still, when looking through the site, disc appears to be the most accepted spelling, and Grammar Girl agrees: "Although there is some disagreement, Stedman's medical dictionary recommends the spelling 'disc' for all medical uses."
"I think I may have slipped a disc," Mulder said as he massaged his lower back. He waved a hand at Scully's silent offer to help and looked toward the woods. "It's more like a bad sprain," he added as an afterthought. "But I'll make it. Let's go find those kids."
The World of Sports
There are a few "thin, flat, circular plates or objects" in the sports world, and Frisbees® is the most recognizable. Disc Golf is another favorite, and Wikipedia offers several more games.
It appears that for the most part, disc is the popular spelling for these flying objects.
"It's called Disc Golf, Daniel," Jack said with an impatient shake of his head. "Didn't they teach you anything when you were in college?"
"The only disc we used was a Frisbee, Jack." His friend rolled his eyes, but Daniel didn't mind. He was used to this stuff by now. "Besides, there's much more to college life than sports."
Disc or Disk
If you remember that disks relate only to a computer's hard drive/magnetic storage, while everything else is disc, you're on the right track. Or, if you prefer, you can go with the "periodic symbol for the element Potassium." Either way, disc seems to be the most common spelling for almost everything.