I'm mostly thinking about 8 bit games, and NES in particular, but it was a thing that continued at least into the 16-bit consoles. There were a lot of games that come to mind that did the perspective shift, sometimes blending genres in the process. Stuff like:

• Guardian Legend (sh'mup with 3rd person action)
• Blaster Master (mix of side scrolling and top down)
• Zelda 2: The Adventure of Link (top down, but sidescrolling battles and dungeons)
• Contra and Super C (change in perspective from side scrolling to top-down / 3rd person)
• Actraiser (sidescroller + god game)
• Battle Golfer Yui (adventure/golf game mashup)

I'm sure there's plenty of others I'm not thinking of. It just feels creative, like even if in some cases a title might not be a "good" game, stuff like this just feels interesting, and there was a lot of experimentation with genre mashups and perspective changes like this in the 8 and 16-bit era.