I used mantids for a research project awhile back. People really enjoyed it. I also notice at Bugfest that people love the mantids. As soon as they see them their eyes light up. Everyone seems to have a mantis story.
Ditto on all the above responses. Perhaps as fellow predator/prey animals we somehow relate to these little creatures because of their forward facing eyes, pronounced head movement, inquisitive nature, forward reaching arms which bring food to their mouths, and in some species the ability to prey on insects, birds, and mammals.
When eating they clutch their prey with both arms, then separate the body holding both pieces in each arm, and are particular of what prey parts they will consume. Often times they will move to a different location while clutching their prey in one arm. They will take occasional breaks while eating and only eat a certain amount, discarding what is left of their prey. Although most would think they are eating machines, they only eat when hungry, and will passively allow other insects to walk right by them or even on them when they are in a state of rest.
They do share certain human facial features like a triangulation between there eyes and mouth. In some species their heads are proportionally distanced above their front arms similar to a human neck. They have unique body posturing that allows them to stand in a prone position with their heads held high or assume a state of rest most markedly by hanging upside down with their front arms in the praying position. While at rest they appear almost statue-like with an occasional slow turn of the head.
Once a level of trust has been established they will freely walk onto an extended hand or accept prey from when offered by a human host. Mantids share other qualities found in other domesticated animals that are cat-like in nature like preening, drinking, using their front legs for striking and clutching prey, along with occasionally falling and striking a threat posture. My cats have done this trick while sleeping on the arm of couch or edge of a bed, roll over, fall, and jump up with tails bobbed.
Mantid owners are also very interesting as a whole in the fact that they tend to gravitate to one or two breeds of mantids. Owners learn to read their mantid's body postures, are protective and pro-active regarding their mantid's health, adopt favorites, and are involved with feeding, watering, housing, and breeding.
I believe they are simply best summed up as noted on an earlier thread as just being "really cool".