Ringarounds can be used for all sorts of tests, but as Ann suggests, they are often used for reference when printing. They provide a visual reference for variations in whatever process you're testing.
I first did one for color to see the effect of different types of color filtration. You can keep the ringaround posted or handy in your darkroom for reference. For color, for instance, if you want to know how far off your filtration is, you can compare the proof to the ringaround.
If you wanted to do one for film testing, you could shoot a series of exposures ranging from two or three stops on either side of what you think is the real speed of the film, and do this same series on five or six rolls of film, adjusting the development time below and above the predicted time for "normal" development. Make contact prints on your favorite paper using the same exposure and development time for all negs, and you'll have a good set of reference prints showing the relation between film development time and exposure, calibrated to that paper. If you wanted to factor in the effect of the enlarger, you could make small enlarged proof prints instead of contacts. If you use more than one paper or different grades, you could do it on each paper you use.