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.
Ecash, created by David Chaum, and introduced in 1993, was a cryptographic bearer certificate, though the underlying instrument was national currency (e.g. dollars). It required a central party to keep track of spends to avoid double spends, unlike Bitcoin's distributed peer to peer ledger. It existed until the bankruptcy of its issuer, Digicash, in 1998.
Many of the themes that surround discussion about Bitcoin were forwarded by Chaum at the time, e.g.
"The choice between keeping information in the hands of individuals or of organizations is being made each time any government or business decides to automate another set of transactions. In one direction lies unprecedented scrutiny and control of people's lives, in the other, secure parity between individuals and organizations. The shape of society in the next century may depend on which approach predominates." source
Bitcoin is the first cryptocurrency, in that it is itself a currency, not a cryptographic derivative of a non-cryptographic currency.
Satoshi Nakamoto mentioned Wei Dai's "b-money" and Nick Szabo's "Bit gold", in addition to David Chaum's "digicash" in early discussions of Bitcoin. The latter was centralized, but had strong privacy properties and was very widely cited, researched, and discussed at the time.
Hal Finney created RPOWs. This is probably the closest predecessor to Bitcoin, because it was actually developed and usable (not just a proposal). RPOWs are "reusable proofs of work". Created by solving hard hashcash puzzles, they are then traded by interacting with a database running inside an IBM cryptocard. It has the ability to prove what it is executing to remote users. Instead of trusting a data structure created by a p2p network, you trusted the secure hardware.
I think the major new idea is using "proof-of-work" to get rid of the need for a trusted central "timestamping" authority that would otherwise be necessary to prevent double-spending.
The question is if that actually works and/or is worth the enormous energy cost. A similar idea was floated once to prevent email spam, but unfortunately email spammers are exactly the people who have lots of cheap (for them) computing resources in the form of bot-nets they can put to "work".
If you permit the term "cryptocurrency" to be understood very broadly, including not just cryptographic but also quantumphysical means of preventing forgery, then one possible answer is 1970 because of Stephen Wiesner's idea of quantum money. Like all novel concepts, there are many ways to look at it. From one angle, one may argue this is not a cryptocurrency as it uses the quantummechanical no-cloning theorem to prevent forgery rather than classical cryptography. Then again, looking back with today's understanding that this property of quantum mechanics is at the core of quantumcryptography, I'd say a broad-minded thinker could argue that in some sense it is a cryptocurrency.