Heh.

I'll join the list that claims the shower is a good place for solving technical and programming problems. Also, occasionally, while driving - I've even pulled over to the side of the road to scribble a few notes to remind me of the solution details later. I read a programming column years ago where the writer claimed mowing the lawn was his equivalent. Always preceded by studying the problem, of course - I think it's how you first "soak" your mind in a problem (umm, no reference to the shower intended), then turn away from it and let your unconscious creative side make connections and solutions.
Although I'm only a low-output hobbyist, I'll claim it is similar for animation ideas (there's never enough time to animate all the ideas) - do some reading, particularly in the subjects you want to animate. Watch live movies - if on similar subjects, so much the better. If you want funny animation, read and watch comedy. Soak your mind in the "problem".
Then just turn away from it and let your subconscious work on it - making connections and solutions. Do something completely unrelated - such as Rasheed's running. Daydream - make up little stories to entertain yourself. I like to keep a little notebook and pen handy for jotting down ideas and observations as they occur. I sometimes get an idea just as I'm going to sleep - turn the light back on and scribble a few notes, go back to sleep - and try and decipher the notes the next day.
However, there are also classical formulas for storytelling that you can use to your advantage to add structure to the creativity. Many books for writers can give you more details.
Many shorter (and even longer) animations follow, for example, a simple 3-part story formula - setup, conflict, resolution.
For instance:
Setup: cat sees bird (what was the cat doing at the time?)
Conflict: cat tries to catch bird (here's where the animator gets creative)
What techniques does the cat use? What obstacles are in the way? (Obstacles may also mean other characters, or the actions of the bird)
Resolution: the cat succeeds or, more usually, fails in catching the bird. Often with funny comment from the bird or the cat, to the audience, as final shot.
Note: all phases, the conflict phase in particular, can be a lot more complicated than this simple example, and may involve a character against their situation rather than character against character. The conflict may even be a "task" rather than a conflict as such.
Of course, once you've got your creative idea, you've got to persist in the work and discipline required to make it into an animation.
Regards, Myles.