Sure, we could look at Galaga if we're to look at our first dabbling into shooters, but I'd wager that a person would have to be near 40 years old ore more if they followed a path of progression and continued to delve into the genre in the early 80's through Xevious and Thunder Force to Gradius and R-Type and Darius and Raiden all the way through to the bullet hell revolution.
I played a scattering of shooters growing up, but it wasn't until the Dreamcast shoot 'em up topic on GameFAQs recommended DoDonPachi to me that I truly became hooked to the genre. Ikaruga came soon after, and shortly thereafter that I became obsessed.
I certainly played a lot of shmups when I was younger, but I did not really get into them until recently. I played a lot of Life Force, Zanac, and Sky Kid (does that count?) on my NES when I was a boy, but Einhander was the first shmup that I enjoyed without reservations. Nonetheless, it was actually playing through The Red Star - with its awesome overhead shooting segments - that convinced me to start adding to my collection in earnest.
I most recently grinded my way through R-Type Final, and Castle of Shikigami III is currently sitting in my Wii's disc drive; so, I gues that I am into shmups as much as any other genre these days.
EDIT: Zanac is awesome. I played it so much right after it came out that I cannot believe that I did not include it originally as one of the great shmups of my youth.
I really have three specific titles that got me into shmups 1. Tatsujin/Truxton on the Genesis got me first. Mostly from playing it with family and the rocking soundtrack. It caused me to get into other titles like 1942, Gradius, and Salamander. 2. Aero Fighters 2/Sonic Wings 2 - this was my college lunch break for two years. It is the first arcade game I stressed to 1cc and finally did it after about three weeks. I downloaded a neogeo emulator and played the game at home so I could show up in the arcade the next day and show the guys up. If I had saved the money I spent in that cab I could have easily bought the MVS cart now... 3. Perfect Cherry Blossom - Caused me to get back into shooters after a time lapse from Aerofighters. Since PCB, shooters have been back in my gaming world and they are not going anywhere anytime soon.
Star Parodier! I stumbled upon a YouTube video of it, and when I saw the PC Engine shooting CDs it was, well, like the kind of thing only bastardized Eastern philosophy and Meg Ryan movies can describe. Like I've known this game my whole life, even though I'm seeing it for the first time.
1. Guilty Gear 2. Dimahoo 3. Wonder Boy III: Monster Lair
I know I've always played shmups casually whenver i could, but i think the game that REALLY got me into the whole genre was Raiden III for PS2, picked it up for like 5 bucks, after i bought that game, I started collecting shmups.
I've still never played the game, but listening to how much people like it and watching some gameplay/screenshots, I realized I might've been missing out never really playing shmups so I went out and bought all the recommended SNES shmups. Space Megaforce is the first one I played through, and I highly enjoyed it, so I guess that was my official introduction to the world of shmups.
I'm known as ZebetiteGlitch or Zeza Von Thantos on other platforms.