http://www.evehq.net Everything you could possible want and more (sometimes a little too much more)
http://evemon.battleclinic.com Training skill planner, good starting place, a must have for all pilots.
EFT - The EvE Fitting Tool Forum link for latest version. You WILL need this.
EVE (CCP Offical sites)
http://www.eveonline.com/ Exactly what it says on the tin, offering a free 14day trial, however leave me a message and I'll hook you up with the extended 21day trial.
http://wiki.eveonline.com/en/wiki/Main_Page The internal EvE wiki, there are other wiki's but in theory this one is the most accurate
http://evemaps.dotlan.net/ A useful place for information and maps of systems
The Influence Map Also known as the who owns what piccy thingy - its pretty!
http://eve-central.com A place where prices are remembered, want to play the trading game?
http://eve-agents.com/ Find an agent, do some missions, earn some isk, buy some ships, come to lowsec...
http://www.evebloggers.com People who blog about eve, there's quite a few...