Which cellular carriers worldwide allow FaceTime calls over 3G/4G Networks? Do any carriers allow for FaceTime video and/or voice calls to pass over normal data channels directly from an iOS device? If not, what alternatives exist short of jail breaking or other gray solutions that would run afoul of the current policies of the cellular carriers? (for example WiFi devices that in turn use 3G / 4G for their connectivity)
Standard, Apple doesn't allow you to make FaceTime calls on a 3G network. And however 4G is often faster then WiFi, the LTE network isn't supported either.

There are however some ways you can enable FaceTime over 3G using Cydia (so jailbreak) or you can use your personal hotspot feature (jailbreak too) to enable this.

UPDATE:
I've tested the method of Redmondpie (with iFile) and with a Belgium Provider (Proximus) it works like a charm!