Other than typos, 301s for previous links or type-in traffic we have only used a supporting domain for advertisement/other marketing purposes that is catchier than the company name and main URL. This domain just 301s to the main domain.
Something like this can be used in print ads, commercials or billboards to get an idea of the traffic resulting from and subsequent effectiveness of the ad. A similar idea is setup with particular landing pages like www.godaddy.com/superbowl.
Using a different domain for this would not create the best brand recognition for the main URL, however. In our case, it's beneficial to use since the URL is the main slogan of the company as well.