I've used a pair of PNY nVidia GS8400 cards for years. Both are single slot PCIe, fanless, and have two HDMI outputs each. They've driven three monitors like a charm.
Recently I upgraded to an HIS AMD HD7850 to add more GPU acceleration to the system for video editing. However, the catch with using three monitors off of a single AMD GPU is that one of the monitors
must be connected to one of the DisplayPort outputs. Furthermore, the connected monitor has to have a display port input or an active Display port to DVI adapter must be used to connect to a monitor with a DVI input. Passive adapters will not work when connecting a third or more monitor.
What complicates things further is that not all monitors, at least in my experience, work with active DisplayPort adapters. I've got a pair of LGs and a single Acer monitor and none of them work with the active adapter (they work with passive DisplayPort adapters and all other sources). However, I have an old junker monitor with no stand that I keep around for testing and it works with the active DisplayPort adapter. Go figure.
I'm not saying AMD cards can't work with three monitors. Clearly they can. There's just some caveats in my experience. From what I have read, however, the latest nVidia cards with 3+ outputs do not require active DisplayPort adapters to work with three monitors. I haven't tried any out but will soon ...