As someone else said, depending on which part of the process you are interested in, depends on what skills you need. You also didn't mention if you were in interested in either the 3D or 2D medium, because a lot of those skill sets differ as well.
The most important skill you "must" have.....the ability to draw. The ability to draw is the most important because the studios don't have the time to teach you how to do that. A studio will teach you to use their computer software (3D or not), but drawing is something that you can begin to teach yourself at any point.
Most studios are more interested in seeing images of things drawn from life and not from your imagination. The ability to draw the human figure from any angle is very important in this profession. The same also applies to animal anatomy as well. Your ability to replicate their characters in not important or are your own personally created cartoon characters. A portfolio of your artwork and demo reel of any animation that you may have created is also required, especially for animator positions.
It is best to attend the best art school that you can afford for animation. Some colleges are of course much better than others, but just getting the basic skills and the chance to develop your personal artistic skills at any art school is so valuable. I attended the Art Institute of Pittsburgh for animation and loved it and just working around other creative people is amazing. It may have not been my best choice for where I'm from, but it was the one that I could afford (don't let me fool you into thinking it was cheap though...it was not.) You could google animation schools and the area that you are from and see whats close to you...there are Art Institute schools all over the country, there is Full Sail (which I believe can be completed totally online), Cal Arts (Disney originally founded this school to help its animators develop), etc.
Another skill that this field requires is persistence and hard work and as someone else mentioned, the ability to find work once the project you are working on is finished. There are very few animators that actually have full time jobs and they are usually the lead animators at each studio, they are the ones that the studio cannot afford to lose to the competition. Sometimes, if the artists are lucky, they can moved onto another already started project or onto a project that is about to start into production, but this doesn't always happen for everyone.
I once heard Disney animator, Glen Keane say that if you really want to work in animation, you have to live it. Everything you do has to revolve around animation and becoming better.
The more effort you put into it and the more you are willing to push your artistic abilities in directions you are not comfortable with, the better off you will do when it comes to finding a job. My weakness is the human face and even now, years later, I still fight with it....but I dont' shy away from trying to working on them, I look at the way that different artists (animators, comic book artists, and traditional artists) work with portraits.
I wish you luck in whatever you choose to do and cannot express to you how much fun, excitement and frustration you will experience if you decide to go after this. Its an amazing ride.