Most likely cause (at least the easiest to determine and fix) is the phono jack.
Unscrew the protective plastic cover from the metal part of the jack.
Check the solder joins and make sure that all are still secure.
If yes, then you may have a blown speaker or a short somewhere along the length of wire.
Test this by listening to something in stereo and rolling the wire between your thumb and index finger. Start at the end of your phono jack and work your way up the lenght till you get to the part where it connects to your headphones.
If you find a spot that consistantly makes crackles or kills the sound in either speaker you found your short.
Snipt the wire on either side of the break. Repair by joining the two ends by soldering them. If you use shrink tubing, be sure to put in on BEFORE you solder.
If you aren't using shrink tubing, than you take great care in using electrical tape (which is by far not as good as shrink tubing).
If it isn't the wire, you may have to contact the manufacturer to get a new speaker for the flakey side. Take apart the head phones, and solder the new speaker to the contacts.
Carl