What cryptocurrency systems predate Bitcoin, and how do they differ from it? Although Bitcoin is certainly making strides as the first cryptocurrency to enter (comparatively) widespread use, cryptocurrency has long been a topic of discussion in fiction and academia.  What cryptocurrency systems were in existence prior to Bitcoin, and in what specific respects do they differ from it?
The closest predecessor to Bitcoin is generally agreed to be Wei Dei's b-money proposal.

The proposal had a lot of holes. For example, it assumed that money could be created simply by solving hard computational problems. But it contained no mechanism to control currency inflation, so currency would inflate as computing power increased.

He actually offered a way around this, auctioning off the currency. But this still creates huge problems without a centralized authority -- who confirms the bids were paid and issues the currency? On what authority?

It also hand-waves over major issues. It requires servers to be partially trusted and argued that to be a server, you could be required to deposit some money in a fund that would be debited in the event misconduct was discovered. But who would debit the account? And who would get credited? And by what authority would they do this?

But this got the ball rolling on the idea of a completely decentralized crypto-currency. The amazing thing about Bitcoin is that it solved all the remaining problems at once.