My DS is sleeping on his right now. When he was younger, I would put it either in a basket or in his car seat in the living room or where ever we were hanging out so I could always keep an eye on his movements. Now that he is a bit older (6 mos), I put it in his crib for naps and in the family bed at night. It is a short hair one (clipped to about 1" or so, not long and fluffy but super cozy just the same) and I don't worry about it a bit.
Happy mumma to my boys Henny Tom (Nov 30, 2008), Arlo Odie (Oct 5, 2010), and baby SISTER! due mid-Dec 2014.