Not really sure. I always liked playing them at arcades when I was a kid. Galaga was probably the first one I played, but I don't really know.
I had this sampler disk on PC in the mid 90's called "Wings of Thunder" that had like 20 or so games featuring ships / jets / etc, at least half of which were shmups. (a lot of Apogee games)
Galaga like many of you... but also Last Resort! I dropped a LOT of quarters on the game as a kid.. that game was pretty important for me as far as getting into shooters.
This is a good one though I always thought it was hilarious how the transformed robot sprite doesn't animate at all. He just sort of strikes a pose and glides through the air without budging an inch.