There appears to be a bit of a communication breakdown in this thread. Everyone is posting ways you can run 3 DVI screens from one graphics card and, smr, you keep responding that people are saying it isn't possible.
To keep it simple, all you need to run 3 DVI screens is one ATI card from the 5xxx series, 6xxx or 7xxx series. The card
must have at least one Displayport output. Let's take this one as an example, as it seems to be the cheapest OcUK currently stock that will work,
http://www.overclockers.co.uk/showproduct.php?prodid=GX-268-SP&groupid=701&catid=56&subcat=1983
You would connect one screen to the DVI using a DVI-DVI cable. You would then connect the second screen using an HDMI-DVI cable (or HDMI-DVI adapter and a DVI-DVI cable). For the third screen you will need an ACTIVE Displayport to DVI adapter - PASSIVE won't work - and then use a DVI-DVI cable from the adapter to the screen.
Alternatively, both ATI and Nvidia cards can run 2 screens per card, so if your motherboard has the right slots you could run 2 cheap graphics cards, hook up two DVI screens to one, and the third screen running off the second card. If you want to run 3 screens off 1 card however, you will need either a Kepler-based nVidia 6xx series card, an AMD card from series 5xxx or later with a Displayport output and an Active Displayport-DVI (or VGA) adapter, or a Matrox TripleHeadToGo card as Purgatory suggested.
I previously had a 5870 that I ran three DVI screens from using DVI-DVI, DVI-DVI, DP-adapter-DVI. I currently run 3 screens from a 7970 using DVI-DVI, HDMI-HDMI, miniDP-adapter-DVI. I know the AMD set up works easily, hence I'd personally recommend that.