As far as Web Design goes, vector is where it's at. The ability to resize things while keeping the same resolution is invaluable. Perhaps you want a logo on a banner, but then you want it on a business card, and all sorts of versions and sizes pile up.
Messing with this would be a huge pain in pixel art, but with vector you just resize and you're a-okay!
However, smilies are different as they rarely need to be resized, and their small size is ideal for pixel art.
Most of this sites assistance will be irrelivant, however, since this art isn't really
pixel art.
Although, this community is serious about art in general, so some help can probably be provided.
It's kind of hard to critique multiple images though, as it's hard to pick one and critique it and only it. I'd recommend posting a single image and applying anything you learned to everything else privately.
The gradient is nice, but seems a little monotone, since yellow and orange are very similar colors. It's easy to recognize as a smiliey though.
Some simplification could be in order, as such a vast amount of smilies can be really daunting. If you look at the smilies on this forum, you will see that there are (comparitavely) few, but they cover broad ranges of emotion.
Also, the little guy is lovable, but he looks like a weird french fry... *shrug*
EDIT: I'd recommend changing the color to show emotion as much as possible.
Red = angry/passionate
Yellow = hyper
Green = sick/calm
Blue = passive/sad
etc.