I've decided to reformat this thread as a place to post useful EVE tools for everyone from newbies to advanced players.
EVEMon: The ubiquitous tool for EVE Online that everybody uses, but in case you're not familiar with it, EVEMon allows you to monitor and plan your character's skill training progress outside of the game. It's a very useful tool that every player should use.
EVE Online 2D Maps: If your starmap bugs out or in case you want to do any advanced planning out of the game. The maps come packaged in a .pdf file, so you'll need Adobe Acrobat Reader. I looked through them and they seem very handy, as they have all elements in the maps labeled so that you can see the names of all regions or systems at once.
EVE Central: This website takes uploaded market information from players and provides a view of the entire EVE Online market. It helps you to get a general idea of the state of the markets in every region. The main page also links you to several other EVE tools.
BattleClinic EVE Online Loadout Browser: The browser allows you to view and create fittings virtually. Kind of nifty.
EVE Fitting Tool: haven't used it yet, but hear it's a standard. You can create fittings virtually.
EVE Online References:
EVE-GuidesEVElopediaEVEWiki