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EveMon is primarily a skill planning tool, but has some other features as well. It's almost a must have and is widely used.
Download Link: http://evemon.battleclinic.com/
Eve Fitting Tool (EFT) is one of the two most used fitting tools.
Download Link: https://forums.eveonline.com/default.aspx?g=posts&t=24359
All fits posted on this wiki are posted in EFT format and will import straight into the program (once it is on your clipboard)
Pyfa is the other widely used tool. It's Python based, which means it works with Linux based OSs
Download Link: http://www.pyfa.net/
jEveAssets is an asset tracking program, which is especially useful if you have a lot of characters, or a lot of items (or both).
Download Link: http://eve.nikr.net/jeveasset
Evernus is primarily a trading tool, which tracks your buy and sell orders, assets and profits (or losses)
Download Link: http://evernus.com/