For three displays, you need ACTIVE Mini DisplayPort adapters. The only active DVI adapters sold by Apple are dual-link, but there are non-Apple active single-link adapters available.
Single-link DVI is limited to a maximum resolution of 1920 x 1200.
You can use dual-link DVI adapters with single-link DVI cables and displays (resolution not over 1920 x 1200), but single-link adapters are cheaper.
Malcolm has that right. The signal levels have to be boosted up, so the ACTIVE adapters have signal boosters in them.
That table has a lot of the right info side-by-side with things that will NOT solve your problem, so read very carefully. (e.g, [Full size] DisplayPort, which does not fit).
In the US, Startech and Accell ACTIVE Mini DisplayPort to Single-Link DVI adapters are sold in many places, including Amazon, for about US$35.