Gimp if you want raster or inkscape for vector. If you have a tablet to draw with, it's should be pretty good. Or you could also use a scanner.
(I have never tried Gimp before so I don't know how aweful it is )

What kind of map: I think the question could be : world map, regional map, city map, or other kind? Because some softwares are better than other depending what you want to do.