A game that's good for a quick plow-through at a moment's notice is any Metal Slug game, provided that infinite continues are at your disposal. If you don't like the thought of "infinite" continues, you can just imagine the idea of stuffing an arcade machine full of your laundry money. As long as my game binge is not disrupted, infinite continues are welcomed in my house.
After 44 continues (some of those levels are just RIDICULOUS hard), I completed Metal Slug XX with Fio in one sitting. And yes, I found out too late that the PSP game is just a fancier version of the Nintendo DS game I got earlier for the cheap. So sue me.
As a Metal Slug game, it satisfied the run-and-gun urge I had at that time. As for replay, there may be times when I'll try to see if I can best myself, perhaps taking less continues to finish. At one time, I was able to complete the entire first mission without dying - that would've made me do a fist-pumping "hells yeah" in an actual arcade...followed by awkward stares. There's also the side missions where you just play through a mission trying for the most kills, saving the most prisoners, or just surviving.
Bottom line, if you're a fan of the series, you know what you're gonna get: lots of guns, hoards of enemies, and bullets galore.