Is there any free animation software that's good?

You might want to look into Blender. Warning, the learning curve is steep. But it is free.

What @johnpowell said. You might want to check the hardware requirements; everything started insisting on being fuzzy when I installed a proper graphics card.

Wait, are you talking about a 3D modeling program or an animated gif manipulation program?

What kind of animation are we talking about?

A good place to learn how to animate is www.doink.com. DoInk provides free drawing & animation tools via a browser so no downloading of software is required. DoInk has a great supportive community of artists to learn from. DoInk clips can be posted to YouTube, embedded in Facebook, downloaded, etc.

The very best free software you can get is Maya. Here’s information on the free download:
http://www.your3dsource.com/free-maya.html
The free version watermarks anything you produce on it, so it’s good for learning but if you wanted to produce commercial animation later you’d have to buy it.

For now, I’m looking for 2D animation. When I get the hang of that, I’ll move up to 3D modeling. So any programs you think are good would help. I’ll put some on the backburner but I will probably experiment with them in time.

I’m getting interested in scientific illustration and looking at companies that hire after further schooling. They recommend having some experience in animation, and they do a bit of 3D animation themselves. They gave me a list of the programs they use but they’re each like $1,000 so I don’t think I’ll be able to use them until I’m further along my career.

btw, Blender looks super amazing. Just to say