NOTE: I wrote this before your latest post, and have been working on it since then. As such, I will not touch on your walking animation, seeing as I have changed the sprite. It is pretty good for your first animation in GIMP. Also, yeah, GIMP is awesome. I've used it for years. I can't figure out Photoshop... I am also ecstatic to hear that you're bringing out a whole non-recolor Rex, I'm super excited to see him. Rex is awesome.
On the sprite itself though, the thing you posted from another person actually makes a lot of sense. When zoomed out, sprites look pretty. When zoomed in, they look messy, a bit sloppy, and any odd pixel placements become more apparent. That's why final products are left zoomed out, and why you work at a very zoomed in level. It's also why I hate dithering; it looks all messed up when I'm zoomed in.
One (very easy) thing I would do first would be to change the background color behind the sprites. If you look at a lot of sprite sheets, they have weirdly colored backgrounds. This is to keep a white background from being confused with the white on the sprite. On MS Paint, if you were to try and move it with transparency, the face would be transparent too.
It's less complex than it sounds

'.
I'll try to just deal with the 32 bit one, because that's what you say you're continuing. How many colors are in that thing? You don't need half that many. 32 bit lets you have 16 colors. That doesn't mean you have to USE 16 colors. You can probably get away with less than half of that.
This is especially so with gray. Gray is weird. There are a few colors that you really have to push to show contrast. 0000ff(pure blue) is one of these. Gray is probably the most dangerous of these, because, unlike blue, it SHOWS when you get the contrast wrong with gray. As such, it's better to stick to only a couple of colors with gray so you don't fall into pits of "a little too much" or "a little too little" contrasts. When I say this, I'm looking at the sweatshirt more than anything. The colors on the top and bottom halves of the sweatshirt have not enough contrast. But the dark on the right of the sweatshirt has too much contrast compared to the others. Another contrast issue is on the face. On zooming in, I notice that there's a very faint gray used as anti-aliasing around the mouth and such. Normally, this is okay, except that I had to zoom in to see it! It's too faint. That color is effectively invisible there.
That's also why it looks better zoomed out than in right now. When zoomed in, you can see all these barely contrasting colors lined up and it looks weird, but when you zoom out, these colors vanish into their surroundings, and it looks like a single, solid block of color.
Readability: Readability is one of the most important aspects of a smaller sprite. This means the parts have to be easy to distinguish and see. With all of those very dark colors clustered in black, that sweatshirt just looks like a dark mass.
A wise spriter who really doesn't like me once said that a good way to improve the readability of a small sprite is to remove black lines inside the sprite. You can leave it on the outline, but that should be it. Black swallows everything around it. Black within the sprite will eventually eat up your entire sprite's readability. Instead, use the colors themselves to distinguish parts from each other. For example, remove the black line between sweatshirt and pants, using the difference in brightnesses to do the dividing. Along this line, I have simplified everything down to a base color and removed all of the black lines inside the sprite(and I fixed a couple of jaggies, and moved the hands down a bit, but that's it, I swear).

Isn't he charming? I actually think it might be plausible to stop there...
But that wouldn't help you, now would it? Now, see how each part is clearly different from the others? It's readable. You can tell quite easily what each part is(even if we don't entirely know what it is overall). His pose also looks a little more relaxed there too, doesn't it.
From there, you just shade, only using what you need to define the character's shapes, paying special attention to making sure that each section stays distinguished. Also, remember that if you want it to, hair is shiny, so you can put highlights there too, but make sure the hair is obviously still black.
Here's mine:

If you so please, you can cover each part with colors, and that should increase the color count. This will make it seem more like the 32 bit. Most 32 bit sprites have to split their 16 colors through a variety of colors. You only need to split it through one color right now: gray. If you take each part and make it a different color, you get closer to that color limit really fast.

I gave him a tan-ish skin color, a red jacket, blue jeans, white gloves and shoes, and blue-black hair. The far left(simple) one has 4+transparency colors. The middle one(gray shaded) has 8+transparency colors. The far right one, the colored one, has 10+transparency colors, making it distinctly 32 bit.
I hope this has helped. Personally, I thank you, because I hadn't sprited in, like, a month, and this reminded me how much fun it is. I'm actually really proud of the end product I came up with from you base.
Good luck, and have fun!
Edited by Ego, 22 July 2010 - 04:51 PM.