If you're in Europe send it to ukipodrepairs.co.uk there are a few repair companies in the US.
Improved answer:
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I recccomend that you check out apple support on the apple website. If your iPod is "bricked"(meaning it is broken with no chance to fix it whatsoever), you should check out sellmytronics.com. they buy your broken ipod and recycle it and send you a check in the mail.
It depends on what is broken on the iPod.
There is not a way to adjust the sensitivity on the screen of your IPod Touch. If you think it may be broken you can send it back to Apple to have them fix it though.
fix it
No it wouldn't be broken. If there's something wrong with the Ipod, and it does brake, just restore it.
It depends how it's broken...
Impossible
You can send your iPod into Apple and get 10% off your next iPod!
If you are sending in an iPod for repair, they probably will send back the same iPod. If you are applying for the warranty because of a manufacturer defect, it's likely that they will replace the broken iPod with a new one, but that really is a decision depending on the condition of the defect. I'm not completely sure if this is what you are asking, but that is my best answer.
Throw you iPod at the person you want to send it to
u can use apps like Bump or Photoshare to send, or just simply email it.
check your wire, if its not damaged then your ipod is probaly broken.