You break it, you own it. More common corollary: You own it, you break it.
In the old days (pre-economy meltdown), the temptation was strong to toss a busted iPod or iPhone and upgrade to the latest model. Nowadays, you may want to get a wonky headphone jack or even a bad hard drive repaired or replaced instead.
A couple of recommended fixers:
Demetrios Leontaris' company is NYC iPod Doctor and this doctor makes house calls. You can also mail in for repair. They've been fixing iPods since 2001, the year they were introduced. Mail-in diagnostics are free.
Another option is Portratronics. You can mail for repair or go into one of their stores: 307 W. 38th [8th/9th] 8th flr., 2 W. 46th [5th] 16th flr., or 169 Thompson [Houston]. Diagnostics is $9 for an iPod.