How much should I charge per animation?

You can always use a Freelance formula.

http://www.sitepoint.com/freelance-pricing-1-set-rate/

I have a book on how to establish and run your own independent freelancing gig, and they highly suggest using a formula (similar to the one on that site I just linked you to) in order to figure out how much you should be charging.

Take what you think is a reasonable rate and triple it. Then take what you think is a reasonable amount of time and double it.

I'm currently in the indie game business, and I was wondering what would be a fair price to charge per 2d animation to the games I work on? Assume that I have competence in sprites, vector graphics, and making smooth animations. What prices should I give, to keep myself from selling short but at the same time, keeping respect to the budget of the project?

There're many factors to be considered:
- How large is your portfolio ?
- How many (heavy weight) reference projects do you have ?
- What is your level of qualtity ?
- What is your level of awareness ?

Selling a service is just business like every other business. It depends heavily on demand and supply. In business it is often necessary to sell yourself undervalue to get a foot in the door, i.e. to build a portfolio, to get more experiences or to get into the industry at all.

Many artists often create a more or less large portfolio to display there skills, when you don't have lot of references or a portfolio and nobody knows you, it is necessary to create your own first (=no cash).