I've pressed something (and I don't know what) which has made the outlines around my artboards disappear! Any idea how I can get these to return?
Assuming you are on a Mac, try pressing Cmd + R
What happens if you choose View>Show Artboard?
That's one I make every now and then, too: on a Mac cmd-H normally hides your application. Not in Illustrator. Just press cmd-H again and voilà! ;-)
Ah nice one - much appreciated!