Where is the user's profile picture stored in Gnome 3?

Pictures are stored in the folder /var/lib/AccountsService/icons/[user name]

The [user name] is of type image/png format with a size of 96x96 pixels

Under the folder /var/lib/AccountsService/users you have a similar file [user name] that is a .desktop format - for example

[User]
Language=en_GB
XSession=ubuntu
Icon=/var/lib/AccountsService/icons/dad

The Icon= is not created unless you assign a picture in Users and Accounts

If you assign one of the stock pictures the file will contain - for example

[User]
Language=en_GB
XSession=ubuntu
Icon=/usr/share/pixmaps/faces/soccerball.png

Thus –as you can see– just create an Icon= entry in /var/lib/AccountsService/user/[user name] to point to your PNG file or overwrite the icon in the similarly named /var/lib/AccountsService/icons folder

If there is no global icon for the user, GDM will look in the user's $HOME directory for the image file. GDM will first look for the user's face image in ~/.face. If not found, it will try ~/.face.icon. If still not found, it will use the value defined for "face/picture=" in the ~/.gnome2/gdm file.

source http://library.gnome.org/admin/gdm/stable/overview.html.en#facebrowser

For anyone using Ubuntu 12.04 the webcam picture taken during install (if not changed) is simply stored here:

/home/[UserName]/.face

It is stored as a .png file. Go to your View > Show Hidden Files options to see it and access it.