Games that can be played on a handheld but aren’t really meant for it (e.g. most stuff on the Steam Deck) doesn’t really count.
Metal Gear Solid: Peace Walker for the PSP was pretty great.
The first game I bought for the Nintendo DS was Trauma Center. It really sold me on the idea that new kinds of games were possible with the touch screen and stylus. It was also extremely challenging to get the highest rank on each stage. I spent hours playing the stages over and over trying to get the top ranks. The arcade style gameplay was pretty addictive, and it had a good storyline too.
Phantasy Star Portable on the PSP was really good, I think I wore out my thumbstick playing it.
Castlevania: Circle of the Moon (GBA). Being able to grind XP / gear to compensate for my bad platforming skills was amazing. Also this sparked my love for Metroidvania games.
I think the Zelda Oracle games were pretty rad. Easy games to play, and for the truly committed you had cross progression between the two games to complete quests across Seasons and Ages. The two games had completely different maps and dungeons to explore with different items in each. They were a dual release that weren’t just the same maps with slightly reshuffled enemies like the Pokémon games were. I remember trading my copy of Seasons to my friend for his copy of Ages and then checking in with each other to see where we were and if either of us had discovered any secrets that we hadn’t found in our respective playthrough.
half minute hero. the section where you have the duel greaves has lived with me every day of my life.
Zelda: Oracle of Seasons (GBC)
Runner up: Pokemon gold/silver (GBC)Phantom Hourglass and Spirit Tracks were pretty cool. I played both with the stylus because the DS control pad is tiny as fuck, literally painful to use for more than a few minutes.
Same with the Layton games.
Jeanne D’arc on PSP has to be the best tactical rpg I’ve played for pure fun value amazingly polished game if not that well known.
PSP has an amazing catalog I still keep a ton of them on my phone and attach a bluetooth controller.
Dude playing MHFU on PSP with friends was literally peak gaming!
Probably old Pokémon like leaf green and Yoshis island.