Apple iPod 16gb; Can this be used without the internet?
Yes.  You can use your iPod/iPad/iPhone without Internet.  

As long as whatever you are doing doesn't require an Internet connection, you will be fine.

For instance, if you are listening to music that you sync'd from your computer or downloaded from iTunes, it will work.  You can even play a number of games without an Internet connection.

However, streaming services like Pandora, Spotify, and Netflix will not work.