There's a big difference for me between the most beautiful, and my favorite. My favorite fish is Ctenopoma acutirostre (leopard climbing perch) because they are very neat predators that are fun to watch. They are not, however, really "beautiful". As jeuveniles, they are brown with brown and black leopard spots. As adults, they turn to a nearly solid brown.
What I think is the most beautiful fish is probably Turquoise Severums, German Blue Rams, and SubRosa's avatar, which is a type of checkerboard cichlid.
Oh, and can't forget the Gulf Pygmy Sunfish (elassoma gilberti) for prettiest fish in the smallest package.
Wow! You guys found some great fish. A lot of these I've actually never heard of before! And they're all so stunning! BTW, your pictures are all fabulous. Thanks to you few who also did something a little out of the ordinary, to widen my range of options, like the schooling the fish page, or the sun fish, which I've only heard of once before. And to the rest of you who have replied so far, thanks for letting me know about all the amazing variety out their! I always love to learn about some new fish, or a fish I've never heard of before, and you guys really helped! Thanks!