Some questions:

1. It's a dark and stormy night in the North Atlantic in 1942. As
admiral at base, you have just read decoded intercepted Enigma-encoded
messages which detail the time and place of a wolfpack attack on a
huge and important convoy. Do you divert it?

2. How can you flip a coin (fairly) via a long-distance phone call?

3. Can there be a cryptosystem in which everyone can encode messages to
you, and see each other's encoded messages to you, but only you can
decode and read them? What special advantages would any such system
have?

4. Can every imaginable cryptosystem be broken? (One-time pad, quantum
systems, RSA, etc.)

5. Should the government be able to monitor all e-mail (or phone
conversations) in the interest of national security? Should use (or
export) of cryptosystems be limited? Should there be a key escrow
system? 

6. Do you (should you?) have the right to decrypt (and copy) DVD's that
you buy?

7. Can we measure the amount of information contained in a message?

8. How can information be compressed, so that it can be transmitted or
stored more quickly, efficiently, or cheaply?

9. How can information be protected against errors in transmission?

10. How can useful information be extracted from huge piles of data
(for example, from the reams of intercepted e-mails that the
government might pile up)?