You can connect 3 monitors, but one will be disabled. The point of having the 3 ports is to give you options, so you can choose between using DVI or HDMI. Here's a quote from a thread on the NVIDIA forums when someone asked about multiple monitors on the GTX 480
For graphics cards which have a single GPU onboard like the Geforce
GTX 480 or 470, only two displays can be active at the same time even
if the card has three physical monitor connectors. Some cards like the
older version of the Geforce GTX 295 have two GPUs onboard and three
display connections, two DVI and one HDMI. The first two ports, the
two DVI ports are connected to the first GPU and the HDMI port is
connected to the 2nd GPU. So in this case, three monitors could be
supported as long as the card wasn't set to "multi-GPU" mode. But for
pretty much every NVIDIA graphics card, you will only be able to
activate two monitors at the same time.
This is a hardware limitation. I suggest purchasing a cheaper card like a GT 220 and putting that in to add more monitors.