I finally got around to building something: My Phonetic Alphabets.
It's not thoroughly tested yet, but feel free to check it out!
It's kind of fun to free-associate words for each letter, but certain letters (I'm looking at you, X) are particularly tricky. For example, Ben used xylophone for X, which isn't bad except that, over a bad connection, you might just hear the initial Z sound. I have to assume that's why both NATO and Western Union use x-ray instead. (I suppose x-rated would work as well, but would be more awkward when speaking with your call center operator.)
I find that food and animals tend to pop into my head. I'm curious to see what other people come up with.