On the DS, you could close it mid-play and pick up where you left off (Sleep Mode). You can also do this on the 3DS, but I have found that some DS games won't sleep properly when played on the 3DS (Yoshi's Island DS comes to mind).
Is there a way to make sure games enter sleep mode? I was a little disappointed to be quite a ways through a level, then I put my 3DS in sleep mode, and when I cam back 20 minutes later, the 3DS took me to the Home Screen instead of my game.