I have no idea what kind of media your talking about.
If it's a CD or DVD and the disk is in good condition, the problem could be with your drive. If the disk is off center or misshapen, then it would make a whirring noise, not a "clicky noise".
Floppies sometimes go bad, and they tend to make a "clicky" noise. When a floppy drive goes bad, the bearings tend to sound "clicky" also.
What kind of media?
What format is the disk?
What platform "burnt" the disk?
What kind of software? (Ok, the last one is just me being nosey)