Because of EMF radiation, how dangerous is it using an electric razor
on your face and head everyday?  Does it matter if the electric razor
is plugged into 120VAC or running off of a rechargable battery?

Have you considered wrapping the razor in tinfoil to guard yourself? (just kidding)

I don't think you have anything to worry about. Cellphones give off a
lot more radiation than razors, and so far it seems like they are
safe.

Here are some links, in case you want to read more.

Google search words
"electric razors" EMF

Are EMFs Hazardous to Our Health?
http://www.mercola.com/article/emf/emf_dangers.htm

How to detoxify your environment
http://www.detox.org/emf.html

UC Davis Environmental and Health Study
http://ehs.ucdavis.edu/ftpd/sftynet/sn_100.pdf

An electric razor is just a small electric motor.  Folks have been
exposed to larger and much larger ones for more than one hundred
years, and no one has discovered that this is harmful.

The poster of this question may also want to consider that all soil
contains some amount of radiation.  Therefore, you may wish to avoid
coming into contact with the ground.  Also, the sun's rays have
radiation so you may wish to avoid the sun. Perhaps building a room
with lead walls on top of a tall tower would be the best way to live. 
Just don't touch the lead because that has been shown to be harmful
too.

I'm betting that a person qould get a much bigger dose of EMF by
sitting in front of a computer monitor reading these comments than by
using an electric razor for a month.