Eve Survival
Rats, mission information, and possible loot are listed on this site. Depending on mission, sometimes there are ship recommendations, damage profiles and youtube videos of other players completing the levels.
Originally posted by Nints (Junior Officer)
Cerlestes Ore Charts
This site will provide all miners with great information on current ore/mineral prices, and what to mine where.
Eve Boards
This site will allow you to look up corps/alliances who have registed with Eve Boards (its free!). These will track implants, skills, and progress for others to see. Good tool for comparing skills with other pilots, and seeing how you want to go forward.
The Altruist: Know Your Enemy
The Altruist is your bible for anything PVP.

Dotlan - Eve Maps
Browser-based map system for Eve Online which can showcase ships killed in last hour or 24 hour, local asteroid and ice fields, and station services.
This website shows the profitability of different blueprints, and can also give you a value of your Loyalty points.
Eve-University Wiki
The E-Uni Wiki is a great tool for new and veteran pilots to read up on all aspects of Eve-Online.
Alpha-Clone Friendly Cruiser Fits
Alpha clones are new to EVE Online, and offer people a free-to-play atmosphere. The link above allows Alpha Clones to know what some of the optimal fittings for each racial cruisers are.