Is it possible to run two separate video cards?

You absolutely can. This is how SLI and crossfire use to provide high end (read expensive) graphics.

Yes it is possible to run multiple video cards assuming you have the motherboard architecture that will allow for it. This can mean anything from having SLI-capable motherboards which allow you to run two PCI express cards in tandem, or something like I am running on an older motherboard where I have a PCI video card and an AGP video card running at the same time so that I can still have my multiple monitor set up.