Well, since some mentioned R-Type and Raptor...
Try
Touhou Project. It is one of the best, if not THE best, Doujin Shmup series ever. It is not military, though.
It is a "Danmaku" or "bullet hell" kind of Shmup: Only a very small part of your character, known as a Hitbox, is actually vulnerable and the screen will get literaly buried in enemy bullets through which you need to maneuver your Flying Miko Loli. The scoring system is pretty complex, so you will need to look around the 'net (or ask the comunity) about it once you are able to 1cc the damn thing and want to start playing for score.
Note that all the assets on the main games are done by a single japanese guy, so while some areas really shine (like the music) other areas are really crappy (like the official character art). At least he is getting somewhat better at drawing the girls.
Ah, yes. That's another point you may dislike: EVERYTHING in the Touhou series is a seven-hundred-years-old Loli, from the main characters to the bosses to the normal enemies inhabiting the stages. Every single bloody thing. That means the western Touhou comunity has a greater than normal Girl-To-Guy rate, but also that it has a greater than normal lolicon-to-normal and otaku-to-normal rates.
The games also have an amazing comunity if you are into meeting weird people. The games are being translated by the fans, there are thousands of fan works (from fanfics and fanart to musical arranges and entire games) and from time to time the comunity can get spooky levels of fanatism - The Fallout fanatism in The Codex is nothing in comparison. The comunity is so amazing that if you like the Touhou-verse you will never get bored or find yourself without nothing to do, and some of the "Fan games", Scarlet Weather Rhapsody and Touhou Soccer 2 being the main examples, are pretty amazing in their own right.
The following links are some videos of my favorite stages from my favorite Touhou games. Note that the non-boss parts of some videos may be fast-forwarded, since the main attraction are the boss fights.
Imperishable Night, Extra Stage.
Embodiment of Scarlet Devil, Final Stage.
Perfect Cherry Blossom, Final Boss. Played (abused?) by GIL, one of the better Touhou players ever.
Shoot the Bullet, Stage 10-8.
That's enough. Give them a try, there are demos floating around and neither the Torrents nor the Direct Downloads are hard to find. You can later buy them if you want to support a pretty amazing one-man-developing-team.
And since we are talking Danmaku Shmups, there we go with some other ones you may like:
Exceed 2nd Vampire Rex, Last Stage.
Trouble Witches, Fifth Stage. They are making an English Version of this one, i believe.
Gundemonium Recollection, First Stage. Amazingly dificult game, even in novice mode. Pretty awesome, though.
Gundeadligne, Third Stage. EVIL game. It will make you cry a lot. Made of pure, hot awesome.