Eschatos
Quite possibly the best shmup ever made (or at least top 3), but only those who follow import console titles will know about it. It's a bullet hell shooter, but plays and feels radically different from every other such game out there, and ends up feeling like it got the best of both worlds from oldschool shooters and bullet hell. Everything about the games design just feels good on a fundamental level. And the soundtrack varies from rad to
beautiful.
The King of Dragons
Maybe has more of a following than I'm aware of, since it was an early Super Nintendo port, but I almost never hear this game mentioned compared to the games it later inspired (Knights of The Round, and the Dungeons and Dragons Mystara games). I really wish more 2d beat em ups played like this game, it's more about side stepping and blocking random enemy attacks on reaction rather than zoning out enemies or abusing ai loops like other beat em ups, and in some ways feels more like a modern action game. It's also got the awesome pseudo Dungeons and Dragons aesthetic that Mystara would later run with (it even goes so far as to refer to the devs as "Game Masters" in the credits), and its got music by Yoko Shimmomura whom some of you might know as the composer for Street Fighter 2, Parasite Eve, and Kingdom Hearts.
Dungeon Magic/Light Bringer
Similar to the above, it's a DnD themed arcade beat em up by Taito that almost nobody seems to have heard of, and plays with the formula even more than Shadow Over Mystara did. The combat is like your typical beat em up, but the game has an isometric perspective, and instead of being linear each stage is a dungeon maze with multiple paths, secret rooms, treasure, traps, etc. It has a real feel of exploration and adventure while keeping in tact the tight arcade style action game feel.
Vanguard Princess
Really unique fighting game with a very cool 2 person fighting mechanic, but almost nobody outside of Japan's doujin crowd has played it seriously due to the lack of any kind of built in or convenient netplay.
Elemental Gearbolt
Dark and beautiful lightgun game
Alundra
Basically a 2d legend of zelda with a very dark but awesome story and incredibly difficult puzzle based dungeons. Oh and you can jump without the Roc's Feather, so that's a plus.
Contra Shattered Soldier
I think people tend to forget about this one, but it was the true revival of good Contra games before Contra 4. It has a similar "boss rush" style of gameplay to Contra Hardcorps, but while I never found Hardcorps enjoyable, Shattered Soldier was really fun to me because the bosses felt a lot better designed and the stages more interesting and varied. Also another great soundtrack.
Maximo: Ghosts to Glory
3d spiritual sequel to Ghouls and Ghosts. It manages to pull off a lot of things in 3d that are even now mostly relegated to 2d, and it's incredibly fun.