Is it possible to screenshot a window without the frame?

You can use custom screenshot area.

Press Shift+PrtScr, then select the area you want.

There is an application called Shutter. You can use it to take a screenshot of a specific area, window, your whole screen, or even of a website – apply different effects to it, draw on it to highlight points, and then upload to an image hosting site, all within one window.

You can download the software directly from Ubuntu Software Center. Search for Shutter.

You can also go to this link to view the installation instruction.

To exclude window decorator, go to:

Preferences -> Advanced -> Window Capture:

then uncheck Include window decoration when capturing a window

Also when you run the application, you can click on the Selection button to select a specific part of the window.

If you want to customize shortcuts to make it more suitable, thanks to User: Redbob for pointing it out, have a look here.

Yes, and no, depending on several factors. Applications which use client side decorations will not be able to hide the frame.

To take a screenshot without decorations, when it is possible to do so, you can run the screenshot tool from the dash (or gnome-screenshot), and select to Grab the current window, and then un-check the options for Include the window border.

You can also create a custom keyboard shortcut so that pressing the Print key, will open this app instead of automatically saving a screenshot, in System Settings.