Can I buy or sell with bitcoins offline? Is it possible to buy or sell something using Bitcoin, in an offline mode?

In other words, if I had my wallet on my mobile phone and I wanted to send or receive money from another Bitcoin user who also has their wallet on a mobile phone, can we send/receive bitcoins offline to each other and then later re-sync the transaction to the network?

I find offline mode critical for this currency to progress beyond a simple crypto-currency experiment because relying on the network means that if network access is unavailable, your wallet is useless.
Take a look at Bitcoin apps available for your mobile phone. Several are recommended in answers to question Can I send bitcoins with my mobile phone?. Look for apps that offer some kind of offline mode.

For instance, the highly recommended Bitcoin Wallet app for Android mentions in its feature list, "Enter transactions while offline, will be executed when online".