This used to be one of my primary concerns when I worked for the Chief of Safety of the Air Force in the 1990s. What we tried to do was not only identify the most common types of accidents (especially fatal ones), but also to get some insight into the ways military accidents differed from those in commercial operations. However, that had to be done in consideration of the needs and issues of the whole spectrum of aircraft in the Air Force inventory. They rarely aligned particularly well, meaning we had to try to prioritize which problems were most likely to affect readiness in each fleet and deal with them as practical.
Bear in mind that there are a variety of military aircraft that are to greater or lesser extents specifically intended to carry out certain kinds of missions: bombing, air -to-air combat, airlift (cargo), air refueling, etc. Even the ones that are most like civilian aircraft in terms of how they're designed and flown still can be subject to some risks based on military-unique activities (low-level flying, air refueling and the like).
Fighters bring with them their own headaches in terms of stresses on both the pilots and the airframes -- lots of G-forces, high operating temperatures for the engines, etc. They're also hideously complex beasts with an awful lot of technology crammed under the hood; bear in mind that everything a Boeing 787 has to do in terms of navigating, communicating and keeping its occupants alive has to be done in a single-seat aircraft as well... along with adding in extra communications, battle-damage resistance, and the ability to deliver assorted nastiness to one's adversaries.
On the human factors side, in addition to often needing to fly in a more fatigued state (or under more fatiguing conditions), keep in mind that the military has to consider risk acceptance a little differently than civil operators do. Sometimes, the needs of the mission demand putting aircraft and crews in situations that might not necessarily be acceptable in routine flight operations. (Bad weather sucks for flying, but it can provide great cover; flying in the dark is a prominent risk factor in general aviation flying, but U.S. armed forces in general have owned the night for decades.)
Probably the single common thread that can be found across most military aircraft types and fleets is the threat of controlled flight into terrain (CFIT). Military parlance for this kind of accident used to be "collision with ground," which might be a little less precise but was a lot more apt.
There are lots of time when a crew wants to go unobserved, or delay being seen. Fly high, and radar will see the unstealthy; troll around under a cloud deck and anyone with working eyeballs will see you. So, almost every fleet has a need to fly low. Flying low means there's a lot greater chance of hitting something on or sticking up from the ground. A long time ago, one of my Navy colleagues showed me an admiral's operational note to his flyers that's always stuck with me: "Remember -- when trying to fly as low as possible, the best you can do is tie the record." (Crunch.)
I can't say it's "the most common cause" of mishaps, but CFIT can show up in almost any operational community. Apart from that, the issues vary widely by fleet. Bombers, tankers and airlifters don't go out of control very often, but often run into the kinds of landing problems experienced by civilian large-frame aircraft. Fighters might have a shade more mechanical-type losses simply because lots of their components are constantly being stressed, even in normal operations. Finally, the need for quick decision-making in lots of cases is accompanied by having very little time or opportunity to deal with the consequences of bad judgment.
For all of the reasons listed above, I can't honestly say there's one thing that stands out above all others as a common cause of accidents for all types of military environments in all operational environments. The challenges of military aviation safety are to identify themes and trends, look for the opportunity to make an investment in safety do double-duty as an investment in readiness or capability, and react to new hazards associated with new environments as they are encountered.
