In the Marine Corps we have MCMAP. Its basically Kickboxing 101 meets Grappling 101, some police like restraint stuff, dirty stuff like (eye gouges, stomps, open hand strikes, groin kicks) weapons defense, and weapons training(Knife, baton, rifle & bayonet, garrote, improvised weapons). Its much better than what was trained before and fairly complete, albeit relatively basic. Training is supposed to involve a lot of conditioning, sparring, hitting pads, training in full gear and uneven ground, two on one fighting, or situational one one one scenarios. Such as two guys will be sparring and someone will throw a rubber knife into the mix, the first person to get to it and stab the other guy wins. The philosophy is to use the best weapon you have, improvise a weapon if you have none, and only go unarmed if that's your only option. Its not too advanced and won't make you a MMA champ, but it'll teach you what you need to fight well enough. After all, I don't plan on playing spider guard or using a spin kick in a real fight. Apparently its almost identical to Krav Maga. Most instructors will have experience in other martial arts, and its a requirement to become an instructor trainer(can train instructors).
Problem is how its trained is a matter of what unit you're sent to, i.e. luck of the draw. For example my unit was fairly motivated and would run hard box training sessions when we got big boot(new guy) drops to qual all the new guys up to green belt(the standard for infantry by Marine Corps Order). We would also train it for 2 hours once or twice a week as part of PT, and we'd go fairly hard. We also didn't teach just up to green, we taught the whole syllabus plus whatever other stuff the instructor wanted to ad based on his experience in other styles. The only difference between greens brown and black in our unit was rank(you have to be a Cpl to be brown and Sgt to be black). That said a lot of units didn't do that, after all as a Marine you'll almost never need to go hand to hand unless you messed up bad, that's why we have rifles and pistols. Since the training is supposed to be full contact, a lot of injuries happen for something some see as relatively irrelevant to actual warfare. I mean if Pfc Moron hyper extended his elbow because he didn't tap soon enough, or LCpl Idiot got his knee busted with a low kick, well, those are two marines that can't go on patrol. Therefore a lot of units just do half @$$ box training when they get a boot drop just to qual people as a "check in the box" deal. Its really up to your Battalion and/or Company commander.
The Army has something called MACP. Which from what I've seen is almost intermediate Brazilian Jiu-Jitsu with very basic kickboxing, and Kali weapons techniques. Their system seems to have more grappling, but a striking and weapons training. MCMAPs equal parts grappling, striking, and weapons, MACP seems to be almost 70-75% grappling. Then again I've never trained MACP, I've only seen the books, so I don't really know. Maybe an Army dog could give you more insight on it.
I have no idea what the Airforce, Navy or Coast Guard trains, if anything. I'm sure their bad@$$es like SEAL teams and Combat Controllers get some hand to hand training.