Does Nvidia GeForce GTX 260 support 3 monitors?

The monitors have to be the same connector, from what I know for that card.

Nvidia did not start allowing for more than 2 monitors on their single GPU cards until the 600 series, so no, your GTX 260 does not support 3 monitors, you can only support 2.

If you want to connect a third display, your options are:

A: If you have a newer system with integrated graphics, you may be able to run the integrated graphics along side your GTX 260 and have the integrated graphics run one of your displays. This doesn't work with a lot of older motherboards though.

B: If your motherboard has a second PCI-E x16 slot, you can buy a second graphics card, if you are just looking for basic display on your third monitor, just get the cheapest Nvidia card you can find to run that third display.

C: You ditch the GTX 260 and upgrade to a newer graphics card, both AMD and Nvidia offer a number of cards that are faster than your GTX 260, and can support at least 3 displays.