Audacity back in the day. I think it even made my first-ever 50 Sites list. With all the great recording apps out there, I have not had a reason to use it in years, but I still think that a web-based audio recorder has merit. Twisted Wave is as good as any. It is simple enough for young student to easily use, and robust enough to support and export good audio.
This is a great tool to use when you need audio feedback from your students - such as in a world language or speech course. Oh, and it links to Google Drive, so that is always a win-win!