Quote: " Some of the best detail work in normal maps are handpainted!"
more often baked down from a sculpt or high-poly model. While you certainly 'can' hand paint normals, it's a lot like using mspaint... more work than it's worth for decent results. there are better tools with far easier workflows. doing some manual cleanup work after the bake is common, but should be pretty minor.
crazybump, photoshop's nvidia filter, etc can be good for adding fine surface detail to an existing normal map from an existing image if you don't want to model in every little thing, but the meat of a normal map should really be produced through baking, and major forms should be left as modeled geometry.
texture map (I'm assuming this means the diffuse: basic color texture) is very commonly hand painted though, and the specular should be produced using the diffuse as a base, as it is very important that details present in the diffuse be matched identically in the spec for best results. To produce a spec map, I generally convert the diffuse to greyscale, adjust the brightness/contrast and work from there.