TCP and UDP(sometimes) use a simple checksum to make sure the contents are correct.
What I want to know is any empirical data or estimate, of how often a packet is corrupted, but has the correct checksum for a person with a standard computer and internet connection.
Now I know that this probably all varies widely with ISP quality, hardware quality, and more, but I just want to hear any information on this.
You're asking how long a piece of rope is. In general, unless there's something wrong, the error rate should be less than 10-7. On the other hand, wireless, 3G, and such can have significantly higher error rates.
This Google search will show you there's a lot of literature.
From Microsoft Research,
Traces of Internet packets from the past two years show that between 1 packet in 1,100 and 1 packet in 32,000 fails the TCP checksum, even on links where link-level CRCs should catch all but 1 in 4 billion errors. For certain situations, the rate of checksum failures can be even higher: in one hour-long test we observed a checksum failure of 1 packet in 400. We investigate why so many errors are observed, when link-level CRCs should catch nearly all of them.
http://academic.research.microsoft.com/Paper/22436.aspx
Basically transmit 100MB+ over a typical Internet connection and you are very likely to see a silent failure.