In referring to the Burqa bans contemplated or actually in place in Europe, USA Today includes this picture and uses the phrase "face veil".
Burqa bans grow fashionable in Europe, B
y Jabeen Bhatti and Aida Alami, June 27, 2010.
Another term used for these things is "headscarf."
Let's define some terms here—this is a headscarf, as worn by the Queen of England, in an informal outdoor setting.
This is a veil, as worn by Ethel Kennedy at the funeral of her husband, Robert Kennedy, who had been shot by an Arab immigrant:
What the modern Islamic woman is wearing is more like a Ninja mask. Not a veil, not a headscarf, a mask.
As such, the burqa has frequently been used for purposes of terror and armed robbery, frequently by men. So if we don't ban burqas, we may need more veils.