Sprites are just bitmaps, usually with transparent regions, so I assume that professionals use existing paint packages. About the only thing I could see a tool adding to the workflow would be the ability to flip back and forth in the frame set and check the animation smoothness, but I think Photoshop and other paint tools already have some capability for you to do that (i.e. you can quickly save a range of images as an animated .gif and play it back, or something along those lines).
Edit: I also remember tools that used morphing to auto-generate bitmaps between keyframes, so maybe you're looking for something along those lines? Another point: some of the sprite animation you see is actually image-capped from animated 3D models.