The best animation software is the one that you have the least problems with, and one that is very easy for you to use. Animation software is used by many different industries, and has many different quality layers. What is the best animation software used in Hollywood? What is the best animation software used by game developers? what is the best animation software used by internet developers? There are many different questions you could be asking yourself. There are a lot of different animation software packages out there that are used for different purposes. 
A big animation studio in Hollywood would be Pixar. Their animation software is in-house developed, and as such is not available to the public. They were a division of Lucasfilm, and they probably started out with some of that studios cgi technology.
Game developers also create their own animation software for certain games, but a lot of game developers reuse it for subsequent games too. Their animation software is typically tied into a game engine that handles visual, audio, and artificial intelligence elements. So what they create is far more then just an animation software.
Now the reason that you are here is probably to learn about what type of animation software you can use for your own personal use. Now you're talking about asking yourself even more questions. Do you want "normal" animation or do you want 3D animation? Adobe Flash is the best animation software for the internet but it isn't the best 3D animation software. Flash is EXTREMELY dominant in the realm of internet video though. The ability to create animation out of pictures and do it fairly easy is what makes flash so popular. Then you can also program conditional elements into your animations to boot. They make for great advertising games that you may have come across on different websites. Autodesk 3ds Max, formerly known as 3D Studio Max, is perhaps the most popular 3D animation software on the market. It's affordable, and effective for the average developer. It allows you to create polygon rendering, and modeling most prevalent in game development. It's been around for an extremely long time (since the DOS days), and can accomplish quite a few different tasks such as creating 3D images, 3D animations, and programmable video game renderings.

Computer animation is achievable by professionals and amateurs alike. It is mostly hinging upon what type of graphical design software you can get your hands on. Graphic design is also a very complicated computer science topic that is constantly studied and researched. Making 3D images takes a lot of very complicated vector mathematics in order to achieve the goal of a 3D object. Just keep in mind that this is an ongoing field of study that is rapidly seeing breakthroughs all the time. There is a big difference between what is commercially available, and what is developed in house by big hollywood studios and gaming giants.
Also worth mentioning is a little graphics application called PIVOT. It is excellent for creating animated gif files in a matter of minutes. It is also very popular among the developer, and internet crowd.
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