Shinobi is one of the pioneers of Badass Platforming, but I admit it is packed with cheap hits. It's a personal favorite, probably due in no small part to nostalgia, but I acknowledge that some people will find it too frustrating to bother with.
Joe Musashi is on a quest to save a bunch of pajama kids who were kidnapped by some weird crime organization staffed by mohawk punks, Mongolians and colorful ninjers. You go through four levels, subdivided into three or four stages each, with the last stage of each level being a showdown against some relatively large boss.
Joe has a seemingly infinite supply of shurikens to huck at his foes, and when they get up close he'll bust out with a punch, sword swing or low kick depending on your current position. You can also move between upper and lower playfields in certain areas by holding Up and jumping; in other parts of the game this is used to move between foreground and background. When Joe has rescued three or more pajama kids, he gets use of a handgun which levels any foe in one hit and penetrates the irritating sword-shields of the Mongolians and certain flavors of ninja; the gun is retained only until you die or clear the present stage, however. You also have one cast of "ninja magic" available per life/stage, an instant death spell that clears the screen of both baddies and projectiles (thus useful as a last-second lifesaver in certain situations).
The game is all about timing and prioritization. Your most fearsome foes are the colored ninjas, each of whom has a movement pattern and attack style unique to their particular color. Later levels require that you quickly react and identify threats that literally materialize out of nowhere, figuring out in the space of a second or two which foe to attack first and where to attack them from. There is an element of try-and-die here, as the game likes to ambush you from the edge of the screen; but there are no random encounters in Shinobi, everything is placed in a static position, and it is possible to learn your way through every deathtrap.
While the first three levels are quite manageable with a little practice, the fourth level is a nightmare of pits and scores of ninjas materializing out of the air to drop on your head while trapped. Admittedly I have never actually completed the game, getting only as far as 4-2 if I recall correctly; however, in spite of that, I feel the good play control, the excellent Yuzo Koshiro soundtrack and the badass atmosphere of the game make it worth an attempt every couple of months or so.
* Gameplay Video