I have two HT's that I bought from Baofeng for emergency use and I don't have a license. I was wondering: is it perfectly legal in the USA for me to be monitoring police and weather channels without a license so long as I don't transmit on any frequency?
Yes, That is perfectly legal, just as long as you DO NOT transmit on those frequency's. It will be just the same as if you were using any scanner, which you could not transmit with even if you wanted to.
In some states it is not legal to have a scanner in your car. See http://www.fireline.org/scanlaws/scanner5.html
In these states, it's not legal to have a ham radio in your car unless you have a ham license because police will consider it to be a scanner..
Apparently it's even a problem for hams that do have a license: http://www.eham.net/ehamforum/smf/index.php?topic=17576.0;wap2