One thing that every Labyrinth fan has noticed is Jareth's "area." Many, many theories have been devoloped, but the one thing that comes to everyone's mind, the one rumor that is prominant in fanfiction and on the List is, is the sock rumor.
In the movie, we see absolutely no evidence to support any argument as to if it's a sock, something else, or very real. Thus, we must turn to prominant fanfiction to figure out what is going on in the King's tights.
In one of the more famous stories, called "The Package," it is theorized that Jareth is a racing goblin, ie, a goblin with a removable package. Racing goblin packages are left under benches, in shrubs, and in other areas for unsuspecting goblin maidens to find, and have been responsible for some of the Underground's more nefarious unions.
In "The Package," Jareth is portrayed as one of these racing goblins. However, it quickly becomes known that he keeps his package in a drawer. Jareth Jr. escapes, and when Jareth attempts to get lucky with a party guest, he's disappointed to find that the pouch contains nothing but a pair of rolled up socks.
So, how does Jareth keep that image up when Jareth Jr. is stuck in the drawer? The same reason he found a pair of socks in the pouch, perhaps? Yes. Jareth stuffs his tights with a pair or two of socks. Now, of course, another possibility is that that's where he keeps his costume changes, but considering he could use magic for that, the socks are the more likely possibility. More can be found on the costume changes, here.
End verdict? I'm 97% sure it's a sock.