How common is it that Christian missionaries come back from their mission trips reporting extraordinary anecdotes?
The short answer is that it is quite common amongst missionaries in today’s times.
Of course it will depend on the missionary in question! Some do not report these types of occurrences. YouTube is a very poor source of information on this subject, since they tend to foster sensationalism.
A certain percentage of this question will be unknown to history since most historical works on missionary activity details the entire aspect of working ing in the missionary field. Miracles would certainly be documented, but would be not singled out as in our modern day YouTube videos.
I believe that in a general manner most missionaries do report what they consider to be genuine miracles.
Over the decades, I have had the occasion of speaking with hundreds of missionaries. Most do in fact, bring up stories about various types of supernatural happenings, but not all!
The Society of Foreign Missions of Paris (Société des Missions étrangères de Paris) actually required a detailed history of their missionary activities if they returned to Paris. These private works usually contain all aspects of working in the mission field, from how they learned native languages, how their diets of people varied, as well as any supernatural happening while working in the missions. I said if they returned because in days gone by most missionaries never returned to France as they were either martyred or died of disease.
Having been at the Société des Missions étrangères de Paris myself as a visitor, the rector told me that the average Catholic missionary in actual fieldwork prior to 19th century did not live more than two (2) years. The number one cause of death was disease.
In today’s society, social media has made it much more feasible for persons in the missions to recount their stories about miracles and other supernatural happenings while in the lands of missionary activities.
As a title of example, Father Giovanni Salerno gave a group of Catholic faithful a series of talks about his missionary activities in the mountains of Chile. I do not know if any of his stories he told us are in any of his books, but he recounted several stories about how the Devil hindered his missionary work in certain villages. The stories are not for the faint-hearted.
Stories of such occurrences are quite common across the board in Christian denominations.
Just as Anne mentioned in her answer and this is exactly what is posted on our local parish doors:
We don’t believe in miracles, we depend on miracles.
The phrase is universal in Christendom!
Other sources of interest would be the biographical lives of saints and/or missionaries regardless of denominations.
Some anecdotes of missionary life are not always as serious as dealing with the forces of evil, some are a little humorous to say the least. Such is the story of the crab, the Crucifix and St. Francis Xavier, who is one of the Catholic patron saint of missionaries