One common problem with webpages which present zooms of the Mandelbrot set is that usually the people who have made them pay little to no attention to the color palette used in the images. This is why you so often see really ugly Mandelbrot set images like the one on the right.
This is often because people use very limited Mandelbrot drawing software which have very low-quality color palettes (often limited to just 256 colors), and even when some software support better palettes, people are too lazy to search for good ones and instead just use the default palette offered by the program. Another common problem is that people don't explore the set enough nor try to find truely marvelous zooms of it.
This, in my opinion, is quite sad. The true beauty of the Mandelbrot set is destroyed with poor color palette choices and not enough exploring.
The XaoS fractal drawing program is an excellent software which can zoom into the Mandelbrot set in real-time and can produce stunningly beautiful color palettes.
Here are some interesting parts of the Mandelbrot set that I have found with that program. I have really tried to bring the true beauty of the Mandelbrot set with these images. Click on the images for a larger view.