I'm assuming your goal here is to disable part of the functionality of your app by having a master list of bogus serial numbers somewhere. Unfortunately there is no per-copy serial number available, and if there were it would be the first thing the bad guys would change before posting your app for download.
Instead you'll need to detect whether your app bundle has been tampered with from within the app. See this question:
http://stackoverflow.com/questions/846309/reducing-piracy-of-iphone-applications
You'll then need to decide how subtly or obviously you want to limit functionality. Probably the best solution would be to do something innocuous but slightly annoying that generates a specific kind of support request, at which point you can gently prod the deadbeat into considering buying a legit copy.
An approach with more false positives but potentially fewer false negatives would be to check if the app is running on a jailbroken device. The downside there is that jailbreakers may well have legitimately purchased your app, so you're alienating honest customers for little to no extra benefit.
For the app I'm working on, which has a big social/viral aspect (I hope), I've decided that potential deadbeats probably have enough honest friends to pay for the server cycles that they're stealing, and it's just not worth worrying about.