How do I reclaim iPhone storage space taken up by ‘Other’?

We’ve been getting numerous reports of users, who have attempted to sync their iPhones after the latest iTunes updates (7.4.x), finding that iTunes shows space on their iPhone occupied by something specified only as ‘Other’. Often, this space may be only small amounts (a few megabytes), but we have received reports of ‘Other’ taking up as much as 4 gigabytes.