Direct drive is the simplest and easiest way to drive a light. Simply connect the power source with your light source, and you have a "direct drive" circuit.
There are a few advantages and disadvantages to doing this. The good things are: quick, simple, and bright! The negative side effects of doing this are: short runtime, curved output (not constant brightness for X hours), and you can decrease the life of your LED significantly. Also direct driving can create lots of heat.
A booster circuit is used when you need more voltage or current than given. Example: Arc AAA.... uses a 1.5 volt battery, but the LED needs about 3.5 volts.
A regulated circuit is my favorite type of circuit for flashlights. You get a nice constant output for a decent amount of time. I would much rather have an output of 20 lumens for an hour, rather than having something direct drive and maybe having 30 lumens for a short while, then significantly decreasing after that.
Another simple, yet effective type of circuit is a circuit using a resistor. The type of output is similar to a regulated output, but not quite as nice. The resistor limits the amount of electricity going to the LED, so the output is fairly flat.
I think the main reason regulated lights are popular is their overall effect. Something direct driven is very bright initially, but doesn't last. Something that is regulated is usually decently bright, for a good amount of time. Also with a regulated light you know how bright it is going to be ahead of time, and can usually calculate a pretty accurate runtime.
Go regulation! /ubbthreads/images/graemlins/buttrock.gif