Vectors are the way to go.
by personal opinion that is.
Vectors are clean and there isn't any degrading or pixels when you work with it.
you can zoom in, depending on the program, to about 6400x without seeing
any pixilation.
inkscape is a great free vector editor, it takes a little practice.
but once you get into it, you'll never look back.
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if you are a fan of bitmaps, then i'd recommend you to gimp or photoshop
as for other 'for pay' editors, i'd take a look at pixelmator. pixelmator is a micro-app that is taking the designer world by storm.
Adobe products are still at the top and prolly always will be. they are the industry standard. Illustrator, Fireworks for vectors, and photoshop for bitmaps.
the learning curve for all of these graphics editors is a little rough. if you are struggling, head over the the tuts+ network.
Photoshop TutsVector TutsHappy designing
<edit : Added More Resources / More Bitmap editors >