I'm a programmer and I make games for calculators (that means basically that all the work I did up to now is some lame monochrome or 4gray spriting, the whole thing usually in 8*8 tiles).
Hey, we're in the same boat!

A short while back I was a hobbyist programmer for the 84+ using z80 Assembly. Besides trying to write an OS kernel from scratch to replace TI-OS, I personally also made a few games using 8x8 tiled graphics, first in monochrome and eventually figured out how to use the sluggish refresh speed of the LCD driver to my advantage to display 3 level and 4 level greyscale (I even wrote a routine for 8 level at one point, but it was too hard to align with the refresh rate to eliminate flicker, and impossible to use in most CPU-heavy games.) I found that most of what applied in such restricted pixeling, however, spoiled me for a while with less restricted pixel art. For one, I had no knowledge of color theory, since I was usually working with at best 4 (greyscale) colors at a time. And, I only knew how to create more of "symbolic" styled pixel art due to being used to such confined spaces. I'll admit, it took a while to break out of that mode. But I think I've at least gotten out of it by now

I think I can, as a result, give you good ideas how how to improve with "colored" pixel art. for one, try to push yourself to keep making larger and larger sprites, using more and more colors (within reason of course -- for example, try to make a 64x64 fighting game sprite using 16 colors.) While it's generally not a good idea to shove this at pixel art newcomers, I've found that showing it to newcomers who came form 84+ pixel art needed it; it shows some very basic techniques you'll want to know that you probably never learned before. Derek Yu's tutorial is pretty short and only goes over the concepts very quickly, but other than that it's what I recommend reading for starters:
http://www.derekyu.com/?page_id=218And, it also helps if you practice your traditional art abilities on the side. I've found that once I practiced/improved with pencil art, my pixel art improved as well.
Anyways, sorry for being so offtopic

I might as well critique your latest character after making a wall of text not related to your actual sprites and tiles. I agree that the dithering in the tree is way overused; also, the highlights are rather bright, I would tone them down in luminosity some, they're incredibly contrasted to the darker shades in the objects. As for the walking sprite, it's rather hard and since it's "symbolic" it's harder to give tons of advice on it (there's only so much you can do in an 8x8 space), but I guess I'd advice for the top pixel of his "foot" or "leg" that comes forward during walking could be removed, and in the back leg I would urge you to play around with less pixels used.