Edit: I realized I didn't really say why you might want to use Perlin Noise. Here's the short list:
* Context free; you don't need ANY previous data points to determine the value (and possibly the derivatives!) at a point. This is huge, and is the source of 90% of the popularity.
* Gradient (Perlin) Noise has zeros at every integer lattice crossing (i,j,k,..) where i,j,k,... are integers. This means you can add it to an existing time or spatial dataset and you won't disturb the actual datapoints, only add noise to the interpolation between your data.
* Approximately frequency band-limited (Hard highpass at the
lattice spacing, soft roll-off lowpass above that)
* When used as a summation fractal, good approximation to a random walk/fractional brownian motion. This is useful everywhere..
The things above are useful in many models, some having nothing to do with graphics!