Yes, they do.
Our family avoids all of them. Particularly ones that are involved with food in some manner.
I had been pooh-poohing questions about BPA (Bisphenol A, a component that leaches out of many plastics) that [wife's name] had been putting to me over the years after she received email warning her of the dangers (leaving water bottles in a hot car, etc.).
Well, she was right and I was wrong (not the first time).
There is a science forum on a website that I frequent (free republic) and I have followed the discussions on this subject. They got my interest, and research has convinced me that there may very well be something to this. The biggest danger appears to be heating or storing hot food in the bad plastic (plastic with the 3, 6 or 7 in the recyclable-labeling triangles).
For children and newborns especially, one should avoid these plastics. There are significant and increasing amounts of data (animal and human) that BPAs can lead to sexual hormone issues and obesity.