OK, here are some flash games:
The Company of Myself [http://armorgames.com/play/4918/the-company-of-myself] - it should take you 10 minutes or something. I found it quite nice, personally. Also, it's free and short, so there is that. A platformer with a cool twist, IMO.
Shift [http://armorgames.com/play/751/shift], 2 [http://armorgames.com/play/964/shift-2], 3 [http://armorgames.com/play/1846/shift-3], 4 [http://armorgames.com/play/3810/shift-4] - they are platformers...with a twist. Pretty much literally, as you actually "shift" up and down. Guess which key it uses. They actually tell a story in a succession (or at least have jokes that carry over from previous games), so it's worth playing them in order.
Time Fcuk [http://www.newgrounds.com/portal/view/511754] is a...platformer. Its gimmick is the time thing - you are trapped in a maze with other incarnations of you from before and after...well, you.
I doubt all of these would take you well over an hour (if that much) but I still want to suggest them.
Other than that, what length of time are you after? A game you can finish in one sitting, or maybe something that would take up to day (assuming you devote a day to it, otherwise several sittings), or maybe something you can play a lot but each session would be different? Or more than one of these, I guess.
For more than one sitting, but still short overall
- Mark of the Ninja - 2D stealth sidescroller - a really good game, I'd recommend it a lot
- Mirror's Edge - first person free runner. It's also gorgeous to look at and has a wonderful soundtrack. The game itself isn't much but I liked it, it's also short
- Portal 1 and 2 - if you haven't played them already...though I don't thing they need the intro, they are first person puzzles that use...portals. Portal 1 is ~2-3 hours long, Portal 2 is roughly 3 times as much.
- Bastion - an action RPG. What can I say more? It's cute.
- Breath of Death VII and Cthulhu Saves The World - you can get the two for the price of one on Steam - no reason not to, they are $3, I think. Two RPGs in the vein of old Final Fantasy games. Note that I've never played FF, so I may be mistaken. But anyway, some old JRPGs did look and play similar, I think. The games are like them. BoD is rather short-ish, with CSTW being not only longer but you can replay the campaign in alternative modes. Still, it's not massively long.
- Costume Quest - it's taking after the same games that inspired BoD/CSTW but it actually looks decent. It's also for younger audience - it's like baby's first RPG, the plot is that your sibling is kidnapped by monsters at Halloween (they were out to steal candy that night...) and you have to go save them. And get candy in the mean time. While not terribly complicated, I found it really charming and cute. It took me around 10 hours to beat - that's the main game plus the expansion.
- Antichamber - an interesting attempt at a first person puzzle game. I can't really explain it well, you can look it up.
For games you can play a lot but each session is different
- Heroes - I'd suggest 5 (you only need the Tribes of the East - it's a standalone expansion and the best experience), though 1-3 are also nice if you're not appalled by them being old, 6 is also nice in its own way. 4 is...a slightly different best. If you're new to the Heroes series, then I doubt it would be a huge problem, though, as that's the only thing about it - it's a different beast. Anyway, you can play skirmishes against computers and smaller maps versus 1-3 other players should finish in something like 4-6 hours in total. Max, at least, you could go down faster than that.
- Frozen Synapse - top down, turn based tactical shooter. It's awesome. OK, I don't know how much you'd enjoy it, being in the military, but I found it awesome.
- Dota 2 and other MOBAs. Well, I've played Dota 2 the most (especially if you count the original Allstars in there) but most other MOBAs that use the same system as that should be similar enough. Matches take roughly 45 minutes, rarely do they go over an hour. The games do have a big learning curve, which isn't steep it's just...big. You just need to start playing a hero, then move on to another and so on and eventually you'll be aware of all mechanics and stuff.
- Bindings of Isaac - it's a rather interesting roguelike. Well, that's what I can say, I guess.
- Dungeons of Dredmor - another roguelike, it's full of funny skills and stuff. My first character there was a psionic demonologist who was also an astrologist and knew some Egyptian magic to boot. I liked them. Only if there wasn't that freak accident with trying to banish the demon shopkeeper who was probably, like, 20 levels above me, and then called in two other demons (also higher level) and then single handedly snuffed my char out.
- FTL: Faster than Light - a roguelike-ish game set in space. A whole playthrought probably takes around 3 hours tops, that is if you even get to the end.
