In a scenario where trust is not required, can bitcoin be used as a currency without an internet connection?
Yes, but with cavets.
Obviously, one can use paper wallets or Cascious coins like cash, just as others have pointed out, but it's also possible for two clients not connected to the Internet to transact so long as they can connect to one another.
For example, say you have two parties that both have mesh wifi on their smartphones, and bitcoin apps that will let the user do this (presently, as far as I know, no current bitcoin wallet clients would let the user do this).
Adam and Bob meet sometime during TEOTWAWKI, both have working smartphones, neither has any cell service. Adam has canned goods & bullets for sale, Bob has only bitcoins to offer. Assuming that Adam actually want's bitcoins due to the future outlook of the Internet, they agree to trade using bitcoins if they can manage it. So long as the two apps can connect over the mesh wifi connection, Bob's client can create at least one transaction without needing access to the Bitcoin network, and it can send that transaction to Adam's phone. So long as Adam's phone client has a local copy of the blockchain (or even just the blockchain headers and merkle trees, within risk conditions) it can verifty Bob's transaction as valid. However, in the absence of Internet access, it's impossible for Adam to verifty that Bob isn't some hacker repeatedly spending the same bitcoins during the crisis. The risk then is all Adam's. He may choose to accept the transaction at face value, and forward it to the Bitcoin network at the next opprotunity.
Additionally, transactions can be created in advance that permits such an offline capable client to spend funds many times before it runs out of usable inputs. It is generally assumed that the Bitcoincard hardware wallet would function in this manner on some level, assuming it's more than vaporware.
http://bitcoincard.org/
