I'm pretty happy with the results so far, and I've definitely improved a lot in just a few weeks. A lot of what I'm doing just feels like guesswork right now though, and I know I've got a long way to go.
Here's a character I created called Bubblebird:
This is a house I made. Having trouble especially with making decent-looking grass textures for a such a big area, so I left it blank for now.
And here is a simple 4-frame animated piece I tried for a contest on pixeljoint.com. The oddly shaped body was the required shape of the canvas.
And finally an animation inspired by a random monster name generator. In this case, I got "Hallucinating Mind Cow". This was also for a contest, in which I needed to attempt an Earthbound/Mother style sprite.
Thanks in advance for any feedback!