I decided to add this page because the links from Intel to the approved hardware vendors have mysteriously disappeared.
1. Lenovo Thinkstation P900 - US prices are quite good for used systems.
2. Dell T7610 - I have one of these with a 3120A inside. Probably the easiest system to find at a reasonable price in Australia. Case is deep enough that you can use a P variant (fanless) card with an external 3D printed fan assembly (see eBay). Usually configured with a single E5-2630v2 and a very worthwhile upgrade is to add a second CPU, heatsink and 16GB of memory, almost doubling the processing power for a couple of hundred bucks.
3. Dell C4130 1U rack - I have two of these, and enough 31S1P cards to fill them both four times over. Suitable for FOUR X100 P-variant cards (without fans). When ordering ensure that they send you the correct cables and mount plates for the Phi, since more often they're supplied with NVidia Tesla GPUs. Can be found in large quantity on eBay UK.
4. Dell R7910 2U server - I have one of these with two 31S1P cards installed. CPUs are usually low-end E5-2600 series although I stumped for one with a pair of E5-2696v4's installed for a total of 44 cores and 88 threads. Needs a special riser card to accomodate Xeon Phis but these are readily available.