Most of the retail Mini-ITX boards and some of the industrial ones come equipped with 20- or 24-pin ATX power connectors. The solution for this is to use a DC-DC convertor like Pico-PSU from http://www.mini-box.com/.
Note though, that DC/DC convertors are power rated for combined output of all voltages and depending on your bord/CPU combination you may need to go with higher rated one. Here is an example. We build a demo system on MSI MS-7698 (E350IA-E45) board and measured power consumption of the board at full load. It was around 28W. However, this board refused to boot up with PicoPSU-90 rated at 90W and we opted for PicoPSU-120 rated at 120W!!! to make it work reliably.