Actually, and perhaps surprisingly, yes you can!
You can use the HDMI/DVI-D port for one monitor, and then use Gert's VGA adapter for a VGA monitor, both screens act independently from each other, so can display different contents.
In the future the Raspberry PI Foundation will bring out a DSI (display serial interface) LCD panel, that can also be used independently from the HDMI interface.
Yes. If only the Gert VGA board actually existed (as a consumer product)…
P.S. Re: the DSI/LCD screen. Even though the Foundation hasn't yet released the so-called "official" screen, it is still the case (AIUI) that you can find and buy something on your own and hook it up and it will work.
Which is, not entirely coincidentally, exactly the same as the situation with the Gert VGA board. It's not (yet) available as a consumer product, but if you can somehow get hold of one, it will
And some folks need to stop being fanboys and see the forest behind the trees.
(One of the best lines I've seen on this board lately)