I never had one as a kid, either. I had friends who did, and played the demo units at stores, but didn't own one until probably 1997 or so when I got one at a garage sale, and even then I didn't play it a ton. I eventually gave it to my mom, as she loves playing puzzle games on handhelds, and grabbed a GBA and later Game Boy player for Gamecube. I've found a handful of games to enjoy over the years, but it's never one I've felt compelled to really dive into. When the Color model came out, I went Neo Geo Pocket Color instead, and I'm glad I did. It was the first handheld I really played a ton, and even just today my oldest boy was playing Bio Motor Unitron on it!
There were a couple of Game Boy games that really made me happy, though. The port of Milon's Secret Castle adding in a password function was huge, and let me play it over multipe sessions back before save states, which I was then able to take and beat the NES original. Gargoyle's Quest also is a jam for me. I dig that series a lot, and the first is a GB exclusive!