earth.li started because JonathanMcDowell and others(?), most of whom were then at Keble College, Oxford, thought it would be cool to have a domain to do things with. We needed a domain that would allow all of us to have cool hostnames for our machines. Eventually we came up with "earth", however all the gTLD earth domains were gone. I can't remember why we didn't go for earth.org.uk, which appears to have been free at the time. Perhaps length.
It ended up with me (Jonathan) working my way through the RIPE list of registries trying to think about what would be cool. We attempted to register earth.ie (several of us are from Northern Ireland), but this was rejected by the .ie registry for reasons unknown (probably due to the fact they don't count NI as part of Ireland, despite the fact their constitution does, and that names have to have a resemblance to the organization registering them). We also looked at earth.aq (f.aq would really rock), but again the residency requirement bit us (we currently have an Earthling in residence, so who knows, we may end up with that domain after all). And so we ended up with earth.li, which seemed cool enough and we could meet the requirements for. The original EarthlingsCouncilOfThirteen each contributed £5 and in return had domain names under earth.li pointed at their machines. They also got @earth.li email addresses.
earth.li DNS was handled by some machines within the Oxford domain: orange ran the primary DNS, and feeble was the secondary. www.earth.li originally pointed at kami.keble, with a web page asking people to look at the real webserver which was hosted on heaven.on.earth.li (oakley.keble).
Unfortunately this soon aroused the ire of Oxford University Computing Services, who claimed that this was against the rules despite the relevant rules making no mention of anything of the kind. Nonetheless the network access of orange and feeble was blocked until they stopped running earth.li DNS and pointing earth.li names at other Oxford machines. The rules were subsequently altered to explicitly ban people from pointing external domain names at .ox.ac.uk machines without permission.
The hosting of earth.li was moved to GraniteCanyon for DNS, TopHost for web space (thanks to SimonHuggins for scoring us that for free) with MX handled by Dave Rand and fed to us by UUCP over TCP.
This continued until the opportunity arose for Adrian Chadd to colocate a machine for us in Amsterdam for free. Thus was born the.earth.li, which was built out of various parts found lying around or bought by contributions from EarthlingsEarthBuilders. the was duly taken to Amsterdam and entered service hosting earth.li, but its connection proved unreliable (read: management didn't like this ugly desktop box in the corner and pulled the plug).
After this it was decided paid for hosting was called for. Pair Networks came highly recommended and the email addresses and web space moved to there in May 1999. While Pair were good their email system wasn't perfect (problems with multiple recipients @earth.li, especially when BCC'd). SimonHuggins and JonathanMcDowell (both Earthlings) started Black Cat Networks in September 1999 and in November 1999 hosting of earth.li moved to there (with fully functioning email even with multiple BCC'd recipients. 
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Thus things remained until July 2000, when JonathanMcDowell had left university and was able to build a new the.earth.li and host it with Black Cat in Telehouse (in a Loud-N-Clear rack). By July 2001 when the contract for this ended Black Cat had their own rack in Redbus and so the moved there.
From a social point of view we had our first "birthday party" celebrating the domain (but really more a good excuse to get as many of us together again as possible) in February 2001, 3 years after we'd first concocted our evil plan. We repeated it again in 2002 and thus it has been decreed that so it shall be every year.
In the early days of earth.li many pubmeets and visits to Keble bar in Oxford were de facto earthlings meets, but as we've grown and spread around the country it's become necessary to be more organised about such things, and thus the first "official" earthlings pub meet was held in London in December 2001 to try and help maintain contact amongst us. The next was held in May 2002 to allow people to meet Simon Chatterjee and Juliet Kemp, the two newest earthlings. Another one was held in Cambridge in October following the opening of the railway line from Norwich which made it feasible for Jonathan to get there.
As the Earthlings continue to take over the world, in July 2005 Black Cat Networks employeed its third employee, being another Earthling, DominicHargreaves.