Depends what sort of look your looking for.
If you want something that looks like a photo or maybe a artistic drawing or whatnot, then use Gimp or Photoshop. (Gimp is Free software so you don't have to steal it or pay 300+ plus dollars for it like photoshop, but it can do 90+% of what photoshop can do.) (see my sig)
If you want something that is clean or sharply rendered look into vector-based sort of art. Gimp/Photoshop do what is bitmaps, which means your working with pixels like in a photograph.
Vector based is more like working with points on a graph and with a ruler. There is no resolution persay because your working with points on a 2-d plane. So you make everything with shapes and gradations of colors.
The nice thing about vector-based images is that they look the same no matter what size you want, you could blow them up to a billboard the size of your house and they will still be as sharp edged as if they were .5 by .5 inch logo on a credit card.
Since logos are ment to represent something, like a corporate logo or something like a stop-sign they don't look photo-realistic or "artistic" or anything like that.
Vector based graphics are tended to be commonly used in publishing and professional logo creation and stuff.
see here for the difference
Stuff like adobe illustrator is used to create vector-based graphics. After you make them and size them then you import them into something like photoshop or whatnot to turn them into a jpeg and make a compressed bitmapped image. A goodexample is the ads you see on these forums, like the "Appro High density servers" logo is probably made insomething like illustrator before it was turned into a bitmap.
Just depends on what sort of look you want to go for.
