As stated earlier, 3DStudioMax, and Maya are very good animation packages, however highly expensive, with quite the learning curve.
Two suggestions if you really want to do 3d without spending enough money to get a car.
One is called AnimationMaster by
Hash. It's actually a fairly powerful package with a lot of advanced features for around $300.00. I've used Max, Maya, and Lightwave before, but this one is still one of my favorites. Great for character animation and on the website, you can see many different outputs from this package.
Two is called the 3DToolKit by
DV Garage. Again, a lot of features in a package that's around $100 for the basic setup. Good for mechanical/environmental animations, but for characters, I go back to Animation Master.
On a final note, there was a program called
Blender that is actually free. I haven't tried it in a few years, but at the very least, it might be a tool to see if you really want to hit the 3D world.