What kind of data is best shown in a rose diagram?
Rose diagrams, also called polar bar plots, are useful for showing azimuthal (directional) data. Any dataset consisting of lots of measurements of direction or orientation could be visualized this way.

A common application in sedimentology is visualizing measured cross-bedding azimuths. This can help work out the palaeocurrent direction (that is, the direction of the prevailing wind or current at the time). This paper by Sengupta and Rao has some examples and some data. 

The rose diagram display is also often used by structual geologists, to visualize the measured orientations of folds, faults, or other strain indicators. Here's an example (on page 10 of the PDF) from Twiss &amp; Moores's Structural Geology book.

One way to generate a lot of data yourself would be to find a geological map with lots of faults or dip/strike indicators on it, and then measure their angles (clockwise from N). 

I'm not sure which came first, but I suspect the design was originally conceived for wind data.