In our case, we had created a functional tool that other website owners could put onto their website to perform a specific complex calculation. Along with that tool, we have a link back to a specific section of our website, for further information. (Powered By: OurBrandName)
The result was many targeted-keyword-domain.tld's using the tool and resulting in tons of questionable quality backlinks. (Many were great, edu's, gov's, etc as well)
I considered waiting for the dust to settle... due to the wide variation of effect on our site (many pages were not affected at all), decided to act and learn why it happened. In the end, I feel we learned our branding is not as strong as we thought it is. Time to get back to work on it...