Others have covered the current method of locking combat vehicles (usually padlocks like the American 5200 series though when we were in Afghanistan we sometimes resorted to cheaper ones meant for connex containers), but I thought I might add a little about the early/mid WW2 and earlier vehicles like the jeep as mentioned by /u/Professor_Longdong. Fortunately for Private Snuffy who has lost his jeep key, nearly all keyed combat vehicles of that era used Hurd ignition switches all keyed to the same key, the infamous H700 key. Keying large fleet vehicles the same is actually a fairly common practice in government. Many police departments order their cars keyed to a single key, so that any officer can access any police car in a pinch. Unfortunately, these keys is usually chosen at random, being the key of the first vehicle of that series ordered by the department. The H700 is what we in the locksmith trade would call "problematic". That big peak just before the tip will have a tendency to quickly wear down and function poorly. Similarly, the police department for Los Angeles Unified School District, Los Angeles School Police, has possibly the worst imaginable key for their Ford Crown Vics: a Ford double sided key that has mostly shallow cuts in it... except for one right up near the head, which is cut to maximum depth, so the key looks like this: D#-####
We had school police cars coming in two or three times a week to remove broken keys. But I digress..

Historically, the military has always had a very comical relationship with physical security. Most of their locking schemes are very simple and not really intended to prevent access by even a halfway determined attacker. Largely this is the result of having an overwhelming surplus of uniformed personnel available to stand between intruders and that which is to be protected. If you have three guys with rifles standing in front of a building keeping out the "undesirables", there's not much need for a particularly robust physical security arrangement, especially if it could impede readiness.

Until 1943 the Jeep needed a key to start, but for obvious reasons this was a bad idea: soldiers can be dumb and lose keys like all of us do, soldiers don't care about grabbing the keys when a combat situation breaks out, and keys can fall out of your possession at any time, especially in heated situations. A switch was installed on Jeeps after 1943.
Military vehicles now have a master switch and push button for this very reason.

EDIT: At least at the post I am currently on they do lock most vehicles with a padlock at night to prevent theft during the night when it is more likely. I would assume at a FOB or larger base in a combat zone only a portion are locked, if any, in case of need for immediate use.