Weird as this may sound, there are a few games out there that try to put shoot-em-up into their perfectly innocent side-scrolling action platformer or action RPG. Here's the only two I can think of right now, but feel free to suggest others.

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Edited by Brackynews

Golgo 13. Though it defies the categorization of "perfectly innocent". EDIT: Yes it's part of the main game stages but it comes out of nowhere (Stealth SHMUP?) if you're not prepared for it. Akin to the driving sequence in Bayonetta (god I really just made that comparison didn't I?)

The Simpsons has a little Space Invaders sequence, but I'm not sure if that qualifies.

Space Quest III has a shooter sequence but if it's 1st person that's not a SHMUP either. EDIT: I can't remember what it actually looks like, and screenshot searches were not forthcoming.

Posted by ahoodedfigure
@Brackynews: I'd rather include stuff that arguably qualifies and deal with definition purists than ignore these fine and diverse examples :)