Take a look at the Bitcoin. There's an excellent explanation (pdf) on the official Bitcoin website about how it works. In short: it's money stored as digital data, encrypted with a private/public key schema, with transactions verified not by a trusted third party but by the network as a whole, using peer to peer technology a la BitTorrent. It seems secure, impossible to deceive and impossible to take down.
There's even a stock exchange online at Mt. Gox. There you can trade US dollars via Liberty Reserve to Bitcoins, and vice versa. I put some money in to try and play with it, and once you get past the initial horror of actually getting money into Mt. Gox it's fairly interesting. To get money in you have to transfer money to any of a number of third-party websites that deal with Liberty Reserve. They exchange 'real' dollars into Liberty Reserve dollars. Then I had to transfer from LR to Mt. Gox. From there, you can trade all you like. Just walk the reverse route to get real money back.
It's still in beta stage but I'm very interested in how this will turn out. It has great potential, but it definitely needs to get picked up by more people to ensure its growth. If this currency succeeds though, it'll be a triumph for open source and internet freedom.