I just saw the question Add date range to "Advanced Super Ninja Search Options" for improved general date search options. Those would be great.
A specific useful situation would be finding all unanswered questions that are at least a day old, or a week, a month, etc.
[java] answers:0 sorted by newest will always give a bunch of recent questions first.
A new search option to show only questions that are older than at least a day or two, possibly called
unanswered, would be nice.
//to search unanswered at least a week old. //argument could be simply one of four choices [day, week, month, year] `[java] unanswered:week`
Yes, there is the existing "unanswered" menu item, but it does not filter out recent questions.
Edit: I would like to see a search option like Lance Roberts has suggested