Robert Scoble has the first-order reasons down right.

The second-order reasons are that in any hardware research, you simplify the things you don't care about, and complicate the things you want to investigate.

So it's mainly an expedient decision. It is a good idea if you are primarily interested in Multiple-UAV research, around mission concepts that require loitering, formation flight and coordination, such as distributed sensing, distributed search/reconnaissance, ad hoc communications, etc. It's a bad idea if you are interested in other mission profiles.

Those who work on things like maneuverability questions usually choose single-rotor designs, such as Emilio Frazzoli, who did seminal work on autonomous helicopter maneuvering using a single-rotor model. His robotic helicopters flipped, did barrel rolls etc. Quadrotors would be godawful for researching those kinds of questions. I'd guess that research into high speeds or high endurance would also not favor quadrotor designs. Military missions such as close air support and anti-tank would also probably favor single-rotor designs.

The reason you are seeing a lot of quad-rotors is that there is currently a lot of money in the kinds of multi-UAV research where it is a good experimental design. If the winds shift, you'll see other designs pop up. Basically, in aerospace engineering, the mission dictates the design.

In more real-world scenarios, especially if larger UAVs are needed for applications, there is a good chance that we'll go back to single and twin rotor designs. Quadrotors may actually be used if some good real-world applications using smaller machines can be found.

For the record, I am an aerospace engineer, and I worked in a lab that did quad-rotor work for a couple of years. Fun stuff.