I did an edit of Chomp, hope you don't mind. I'm no expert on any of these fields i'm about to talk, but over the time i've learned the basics, and i'll resume them so it may be able to help you.
Color choice: kept some of you colors (the "mid-tones", middle colors between the lightest and the darkest shades) and tweaked others, by changing hues, saturations and lightness until i achieved a nice contrast. Your original colors where too bleak and close to each other (little variation in hue/sat./lightness between them), one of the most usual mistakes for beginners.
Another important thing to keep in mind is to use a limited amount of colors. This was done in the past for lack of memory reasons in computer games, but that isn't the case nowadays. Still, using a limited palette does help you keep a more uniform look. If you need to smooth out some part of the drawing, just pick a color between those basic ones you have. This is usually done not only in pixel art (which normally is small), but also by digital artists when doing larger pieces. They pick a few basic colors, apply them on an initial rough "shaping" of the piece, and mix them together to blend the shapes where needed.
Volume definition: the shading didn't quite convey three-dimensional shape for the character, it looked like a carboard cutout blob. Shading is one of the most important aspects, if not the most important, in defining the look of the character, giving it depth. I changed the placement of the light source so that i could convey better the shape of it, as an example. You placed the light source in front of it, which is ok but can lead to poor shading (pillow-shading) if not done corrrectly. Even in cartoon and anime style drawings, shading makes all the difference.
Texture: i believe that your inital shading attempt was trying to give texture to the head and "teeth" of the character. But it was chaotic and desorganized, and that doesn't work. It must follow some sort of order for the viewer to interpret it as something and not random noise, as some people pointed out.
Ok, here's a brief explanation of what i changed:
1. Fixed some of the outlines to look more clean (less "jaggy"), and changed their color to a darker shade of the interior color. Change the left corner of the teeth to give it a more round look, and the colors, removed some and altered others. Different shading.
2. Changed the textures. Tried giving a glossy, "metally" look to the teeth, and a furry look to the surface (using only 3 colors for each, would look better with another color but it was just for the example).
3. Added Anti-aliasing and Selective Outlining (look at tutorials for explanations).
9 colors + background transparency color.
All of these things are explained on the tutorials, or on critiques from other works. I suggest you lurk a bit around here, read critiques to other works, and incorporate those in your works.
P.S.: wow, that's a lot of text up there.