Not a class of searches, but a feature: DDG does not have an equivalent of Google's time-based searches (e.g., last 24 hours, last week, etc.).

Hmm... hard to say, but the first thing to comes to mind is programming-oriented stuff. Google tends to find a more accurate hit there sometimes. Google also seems to do a better job filtering out spammy stuff like those irritating portal pottie sites that clone StackOverflow or mailing list content.

My pattern is if DDG finds nothing of value or brings up too much noise, hop over to Google and sometimes it does better. If I can't find it via either search engine it's probably not out there.

I will say that there's rarely a case where Google is worse than DDG... unless you count the tracking and near-monopoly issues but those are peripheral to the core function.