The closest you can get right now is answers:1 hasaccepted:0: note that this won't take answer up-votes into account, and simply orders by timestamp.
A relatively simple enhancement would be a search operator that let you specify answer up-votes when searching for questions: so you could do, say,
answervotes:0 answers:1 hasaccepted:0 and get something fairly close to the "unanswered" list, but exclude questions that didn't have answers at all.
Actually sorting by number of replies seems less useful to me; I'm not sure that the number of answers actually corresponds to anything particularly important. That said, if it could be implemented as a search operator I would love to see equivalent operators for other sort orders: created date, last-modified, votes, views, etc... Currently if you want to specify sort order in a link (as I've done above), you have to use the
tab= querystring argument - which also changes the default for anyone following the link.