You will need an Ati Radeon 5000 series graphics card or above to take advantage of Eyefinity along with 2 or more monitors being able to support the following type of connectivity:

ATI Eyefinity Technology is closely aligned with AMD’s implementation of DisplayPort providing the flexibility and upgradeability that modern user’s demand. Up to two DVI, HDMI, or VGA display outputs can be combined with DisplayPort outputs for a total of up to six monitors, depending on the graphics card configuration and the operating system. Wider display connectivity is possible by using display output adapters that support active translation from DisplayPort to DVI or VGA. 

Example configuration options based on a graphics card with four display outputs: 

The above information has been taken from Ati's Official Eyefinity website.