Planning your character
Fitting your ship
Tracking your assets, wallet, market orders, etc:
These are the two biggest, and arguably the best apps for mobile platforms. They both will allow you to test ship fits, view EVE's item database, and interact with your character's API information including but not limited to: reading EVEmail, checking market order status/wallet balance, skills trained/qued, and list assets. Of course this is determined by how much API access you provide to the applications.
Broski Visual Guides (30 amusing and useful guides to a collection of game mechanics) WARNING: broski is a corp based from 4chan...the machanics in the guides are sound but expect 4chan style humor view at your own risk
Estel Arador Corp This is a link to an EVE Forum thread that details one of the greatest free services in EVE. This corp allows you to use it's standings to create jump clones all over the galaxy.