The beginning of true Shinobi's end, with the console conversion being a very different game and each sequel made for console moving further and further away from what made the arcade games amazing. Still, it went out with a bang and with the two versions being so different, two bangs.
Good thing it wasn't actually the original so we have a handful of other games using that long lost formula. More would always be better though (and some of these are stretching the case).
Rolling Thunder is obviously the original which Shinobi & Shadow Dancer aped to good effect (arcade):
Rolling Thunder 2 (arcade):
Rolling Thunder 3 (console only):
Code Name: Viper (console only):
Dick Tracy (console only):
James Bond 007: The Duel (console only):
Surprise Attack (arcade only):
ESWAT (arcade & console, the console version, like Shadow Dancer, is very different but I actually prefer it in this case, I don't think the original is as well designed as Shinobi despite aping it closely, while the console version is better):
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Sly Spy (arcade):
Shadow Gangs (indie Shinobi wannabe successor)
The console version of Moonwalker is also very Shinobi-like, unlike the isometric arcade version:
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There are a few more like ThunderJaws, it's not my favorite but had cool set pieces like Sly Spy's. Elevator Action Returns is maybe stretching the definition but kinda works, minus the trademark jump action of Shinobi-likes (although not all of the above employ that).
Sunset Riders and semi sequels Mystic Warriors & Wild West C.O.W.-Boys of Moo Mesa also kinda work (with the jumping to different levels of the stage too) but clearly put much more emphasis on the run and gun, going into Contra territory, especially the latter games.
If I missed any notables hit me, I love this gameplay style.