I don't even know where to start. So many truly excellent games went totally under the radar, especially in my time when there were just so many games to play that perfectly great games went by as "mediocre."
King's Field IV: One of the best games I've ever played. Its soundtrack has stuck with me for years. Easily the most approachable and most accessible of the King's Field games, in my opinion, and the dreadful beauty of its world leaves quite the impression.
Return Fire: At its heart, it's a PvP competitive capture-the-flag top-down vehicle-based shooter. It's simple by modern standards, but the mine-laying and helo-rocket-gunning shenanigans made for a real laugh riot when I was a kid. Helped to foster my love of classical music early on, blaring classics like Mars, Bringer of War by Holst and Ride of the Valkyries by Wagner as you demolished buildings and squished their fleeing inhabitants. Plus:
Live-A-Live: The gameplay is nothing special, but it's full of heartful moments end-to-end. I'd go so far as to call this game "beautiful." It managed to get me once or twice. It manages to make a hug between two tiny character sprites one of the most impactful moments I've ever witnessed in fiction. "Beautiful" is apt.
Breakdown: I've said it before, and I'll say it again: this experimental first-person shooter/brawler was one of the coolest games ever made. It's got lots of problems - its Japanese developers really wanted to do a FPS thing, but didn't have a lot of experience under their belts. But they pulled off a thrilling Half-Life alike that I wish hadn't flown completely under the radar. There's nothing else like it.
Kill.Switch: People probably tire of stop-and-pop cover-based shooters now, but this one was the first - and I'd argue that it did it best. It was fast-paced, frenetic, and relentless, rather than formulaic and slow like so many that came after. The action didn't let up from beginning to end, and though the game was rather short and simple, it was satisfying. I actually really appreciated Ubisoft for doing so many callbacks to this game with Rainbow Six Vegas 2: its main character's name is Bishop, and Bishop's armor set was in the game's customization feature.
Shibuya Scramble: This quirky quasi-FMV adventure game had me till the very end. Though the anime it is based on is absolute garbage (in my esteemed opinion), this game was one hell of a ride.
Scratches: This is one of my favorite adventure games of all time. Its underlying mystery was a thrill to uncover, and its atmosphere was phenomenal, shifting expertly from creepy to haunting to nerve-wracking as each of the in-game days passed. Much more than your typical "haunted house" adventure, this game spun a narrative full of red-herrings and subtle interpersonal drama. It had an awesome soundtrack to boot.
So long as you're playing the original release, mind. The "director's cut" utterly ruins the atmosphere, and destroys one of the most poignant scenes in the game (a little music box that just barely manages to miss finishing its tune one last time). I guess sometimes things just need to stay cut.
Gray Matter: Another great adventure game. When people think Jane Jensen, they usually (and rightly) think of the excellent Gabriel Knight: Sins of the Fathers... or perhaps the much less-excellent third game in that series. But I like to look fondly back at Gray Matter, a game I did not play myself, but one that I did watch my wife play. The ending left us both feeling sad, but satisfied. It handled its reveals smartly enough, and the characters were strong. Holding with tradition, the music was exemplary... and appropriately moody. Moody the game was, but not so much as to crush you with its atmosphere.
Front Mission 3: One of the best JRPGs ever made, and so few remember it. Its two-sided story mode hammers home its central message with the force of a sledgehammer: in wars, someone has to lose. Between playthroughs, you watch well-developed characters die sad and terribly final deaths, even though in the other campaigns, they are friends, allies, and even more. It's poignant and striking, and besides this, also happens to be a legitimately fun game to play.
Growlanser IV: Wayfarer of Time: So underrated. A great, fully-fledged JRPG with a focus on tactics and a cast of characters it's hard not to love. Art by the legendary Satoshi Urashihara (I hope I spelled that right) that just pops right off the screen. There's a huge focus on giving the player lots of things to say in conversations. We all know that not every single one of them matters, but you'll be surprised how many of them do. In fact, the game's full of choice points, one of which still haunts my wife to this day (and makes me glad I didn't screw it up, because, man, that hit hard).
Criminally underrated.
I could go on for hours, honestly.