Cypherpunks was a movement/group formed in the early 1990s, founded by Tim May, Eric Hughes, John Gilmore, and St. Jude Milhon. There were various mail aliases and manifestos running around, and in 1992 the cypherpunks mailing list was formed, with the first message being sent by Eric Hughes on September 21, 1992, hosted off Gilmore's infamous toad.com. Cypherpunks is/was the group (or at least a plural), a member of which might be called a cypherpunk.
The core cypherpunks meme was that cryptography, in particular digital cash, reputation systems, and strong encryption, would essentially cause the dissolution of current nation-states. In theory it seemed like a reasonable idea: if the government can't track the flow of money, it can't collect taxes, and eventually they go bust (or at least, lose a lot of their power). Of course property taxes would always be around -- atoms cannot be hidden by cryptography or anonymous remailers.
Occasionally people ask if cypherpunks worry about these technologies being used for "bad things", bad things mainly being defined as something the questioner doesn't like. For the most part, the answer is no; after all, the primary point of digital cash is for tax evasion and the secure purchase of items that your local force monopoly might not like you having (be it pornography, secret documents, copyrighted materials, or damn near anything else that you can fit into a bitstream). More generally, such a concern is not widely held among the techno-libertarians who make up the majority of cypherpunks.
Looking around, it's obvious that not many of the cypherpunk ideals have come to fruition. The first one is that when you want to buy something, you're still stuck with either physical cash, or electronic payment systems which are utterly, thoroughly trackable. Digicash blew through millions of dollars of VC funding late in the last decade, without much of anything to show for it. Part of the problem is that while a digital cash system is easy to write, plugging it into the real world is not. Without the ability to trade digital cash for actual, physical items, it's just play money.
Other of the systems desired by cypherpunks, in particular pervasive strong encryption, reputation systems, and anonymous messaging, have been more widely deployed, but not in areas that the original cypherpunks thought. With the
passage of the DMCA, and strong legal pressure from RIAA and the MPAA, most modern peer to peer networking protocols have adopted these techniques to prevent monitoring and control, not by TLAs, but by media companies. This is primarily because while most people don't care if the NSA or GCHQ is reading their mail, they do care if they get sued for a million dollars of copyright violation damages by a huge media conglomerate.
The cypherpunks list had a near-death experience due to an overflow of spam and crazy political rants, which was not helped by the fact that Tim May seemed to grow increasingly deranged as time went on, with a fairly typical quote being:
"I think we should all hope Al Qaeda manages to get its ANY-59 tactical nuke into place and simply incinerates the entire nest of vipers. A bonus will be the torching of 400,000 inner city negro welfare mutants."
This led to a fairly large contingent of cypherpunks moving to the coderpunks list, which offered some semblance of sanity. Any political discussion was strongly frowned upon there, so nearly 50% of the posts were actually technical. After Tim May quit cypherpunks to go hang out on alt.survivalism, and filtered nodes became available (which provide a feed for cypherpunks with the spam and the worst of the rants removed), cypherpunks has regained some usefulness, but many previous members have moved on to more reasonable lists, though coderpunks has since died out completely. The last physical cypherpunks meeting was in the spring of 2003, though one is now scheduled for August 2004, at Stanford.
The whole idea of using cypherpunks username/password for registered sites comes from the list, presumably created by some cypherpunk long in the distant past, before BugMeNot became usable as a Firefox plugin.