Most integrated graphics will only allow you to run a single monitor. There are plently of video cards that will allow you to run monitors. It would help to know what exactly you're doing with the computer (i.e. gaming on all monitors, playing videos on all, working on some and watching movies on some, etc.) and what types of connectors the monitors use.
Of the top of my head, if you need to use three monitors/TVs, the HD 5770, 5850, and 5870 would all be good. If you need more than three monitors hooked up, you're likely looking at either onboard video (1 monitor) and a single card of the above (for a total of 4 monitors) or two cards of the above (total of 6 monitors). Take a look at the Eyefinity articles here at Tom's for an idea of what you need.