Multifractals: Great Success!
In a rather old textbook I read recently (Texturing and Modeling: A Procedural Approach; though note that I actually have the 1991 edition), the author mentioned briefly at the end of the book a type of fractal called the multifractal. The idea of a multifractal is to actually vary the fractal dimension of the fractal at each point based on, guess what, another fractal map! In a sense, it adds another level of recursion within the fractal.
So why should we care? Well, if perlin noise makes good terrains, multifractal perlin noise makes them 100x better! The explanation for it is simple. In real terrain, we see features like mountains, but we also see features like plains. Mountains have a high fractal dimension, while plains have a low fractal dimension. Perlin noise, in and of itself, has a relatively constant fractal dimension. Multifractal noise doesn't. For this reason, it serves much better for the purpose of generating terrains!
Here's a sample multifractal perlin noise heightmap generated with a home-brewed HLSL shader:
Notice that, in comparison to previous heightmaps, this terrain is far more varied - we can clearly see mountainous features as well as low features.