Cosmology of Kyoto
Simply put, there's not a lot else like it. Not so much a "game" as it is an experience, you get to learn a lot about Kyoto history with a first-person adventure interface and an atmosphere that feels straight up like an early survival-horror game, creeps and all (in fact I wouldn't be surprised if Team Silent played this at some point and it served as some kind of inspiration for Silent Hill....tho I might be reaching there).
You can play it easily on modern Windows machines w/ a specific image that has the DOSBOX set up to run it, and while I normally wouldn't mention something like that here, it's more or less the only way you're gonna be able to play the game in 2018 unless you want to buy an old DOS machine and fiddle around with the settings for half a day to *maybe* get it running.
Gaiares
One of the best underknown and obscure games of its generation, and a pretty early release on the MegaDrive at that. Really neat pod-based powerup system where you sic the pod on enemies to obtain their powers, and a VERY challenging difficulty for seasoned hori shmup players. Some really good music, boss designs and a couple neat anime-style cutscenes too.
Sega Water Ski
Most fun w/ a water-based racing game I've probably ever had, tho it's not jet-ski based like say Wave Race. You basically perform tricks by riding on ramps and between buoys. The physics are really solid and the trick system has a nice range of depth to it. Crisp, colorful graphics and some neat touches for surprises you can trigger give it some character.
Juggernaut
A Myst-like clone of sorts on PS1, made by Jaleco. Not the most original gameplay or story, but the gameplay that's there is nice enough and the story is pretty decent. There's a few solid music tracks in there too but mostly towards the last few areas. There aren't a lot of games like this on 5th gen systems and even fewer on later consoles, and I liked the cyberpunk sections the most as they stood out to me pretty well. The body possession mechanic is interesting, tho I don't think it's used to its full potential.
JJ Squawkers
Just a buttload of crazy shit and hectic action-platforming mayhem with some of the trippiest visuals you're going to find in a video game. And it's a solid-ass game, to boot.
Galerians
Surprisingly good and barely-known PS1 survival-horror game. Like the little brother of RE and Silent Hill no one really remembers anymore. I like it for its cyberpunk-heavy atmosphere and pretty good story. Definitely worth checking out; when I picked it up off eBay about 3-4 years ago (discs only) it ran me like just $20. Not sure what the prices for it are at now however.
Most of my other pics are probably at least somewhat well known or have a huge cult status these days, like Panzer Dragoon Saga and LSD: Dream Simulator, so they wouldn't really need mention here. There are other very obscure games I need to play, though, and hope to do so soon.