Can you transfer Bitcoins from one address to another address directly without going through the web? If you and a recipient both have a wallet on a flash drive, is it then possible to transfer bitcoins from one wallet to the other using a computer without going through the web? 

Example in life: "Here you go nephew, I'll give you 5 bitcoins for your birthday." Then we go to the computer with our wallets and transfer the funds, without waiting for people to decrypt bits and pieces of it across the web, just relying on the local computer.
Yes, the simplest example is that you could create a paper wallet, send coins to that wallet, and give the paper wallet to your nephew.  

In this sense, the paper wallet act similar to a bearer bond. Whomever holds it, has access to the coins. The caveat is that your nephew has to trust that you don't spend the coins (since you have seen the private key).