Klaus Halbach
The Halbach array is named for its inventor Klaus Halbach, a Berkley Labs physicist in the engineering division. The array was originally designed to help focus the beams in particle accelerators. In the picture on the left, Klaus Halbach in 1986 with Kwan-Je Kim discussing a model of an undulator that Halbach designed. 

Klaus Halbach working with rare earth magnets
layout of the 5 magnets used in a halbach array Photo of homemade halbach array.

The halbach array in the drawing above was quick, fairly easy, and inexpensive to build. It took me about 20 minutes to put it all together. It is true that my first attempt was crude and ugly, but I have promised myself that the second one will be much cleaner. A lot was learned the first time around, but more importantly I had a lot of fun trying to coax the magnets into this array. And if fun isn't enough of a reason to justify the monstrosity pictured here, perhaps science is? The most important thing about the assembly above is that it works!

The other cool, and fairily significant feature of the halbach array is that it can be extended by repeating the pattern. Bigger is better, right? Halbach arrays can also be assembled in circles, but would require custom magnets.

Layout of an extended halbach array
So far, the most promising commercial application for the halbach array is the Inductrack maglev train. This maglev technology isn't just for trains. Apparently nasa is also considering it as a means to give their rockets a jump start. Fuel savings could be nearly 40%. There is some good information at this DOE link.
A good article on halbach arrays as they apply to maglev trains can be found here.

Other potential applications include people movers; spark-free mine cars; and high-speed, intercity freight shipments, where sealed capsules are levitated within 1meter-diameter underground tubes.