J.R.
I gave my son a pillow at around 13 months. he started out with a toddler pillow, but we graduated him to a regular pillow. it's a firm flat pillow that's not fluffy or squishy, and i can tell you, he actually uses it :-)
He started to show an interest in them... he would lay his head on throw pillows while watching his baby einstein video, and would cuddle with me with his head on my pillow. And he would ball up a receiving blanet and put his head on it in his crib. clearly he wanted something to snuggle with.
since his pillow is flattened, i dont have any concerns about him suffocating...