What video boards can I put in a 2008 Mac Pro to get 4 monitors (DVI)?
What version of OS X? That'll be your limiting factor on GPU support, I think. The 2008 Mac Pro (3,1) had two 16x PCIe slots, so any PCIe video card supported by your version of OS X should work. The official list:

Graphics cards for Mac Pro (Early 2008)


ATI Radeon HD 2600 XT
NVIDIA GeForce 8800 GT (part number 630-9191 or 630-9897)
NVIDIA Quadro FX 5600
ATI Radeon HD 4870, offered as an upgrade kit


Note: The Radeon HD 4870 card requires Mac OS X v10.5.7 or later for use with the Mac Pro (Early 2008).

Graphics cards for Mac Pro (Early 2009)


NVIDIA GeForce GT 120
ATI Radeon HD 4870
ATI Radeon HD 5870, offered as an upgrade kit


Note: The Radeon HD 5870 card requires Mac OS X v10.6.4 or later and it requires the use of both auxiliary power connections.

Newer cards with OS X support may work, but there are caveats with pre-2010 Mac Pros and I doubt they'd be officially supported.