1. Extra padding for tummy time or learning to crawl.
I refused to buy those ugly, squishy foam puzzle pieces and padded my floor with three yoga mats lined up in a row instead. I didn't move them for several months. It worked beautifully, and it was awesome to practice on, too. (See below.)
2. Photo backdrop. (Capture all of your little one's immobile moments without fussing with a wrinkly blanket!)
3. Giant diaper changing pad. Now that my daughter is almost two, she's almost too long for a normal changing pad on the floor. She also screams "NOOOOO, Mommy!" and runs the other direction when I mention the D word. For some reason, she will actually lay relatively still on one of my yoga mats for long enough to make the change. Right now, anyway. (I should knock on wood.)
Bonus: A rolled up mat makes an excellent (though heavy) telescope.