ActRaiser 1&2. Developed by Quintet and published by Enix, these late 90s city-builders are some of the most unique SNES games out there. The original cartridges aren't exactly worth getting unless you're a tried and true retro purist, so the best way to play these games nowadays is likely on the Nintendo Switch.
Anodyne 1&2. A pair of retro-styled puzzlers from the independent developer Anagesic games, Anodyne and its sequel manage to capture a verry uncanny, almost dreamlike vibe that is mostly associated with older games. They're both available on steam Here, if you're interested in playing them.
Alundra 1&2. Made by Matrix Software and styled after the Legend of Zelda series, these puzzle games for the original playstation have a perfectly cozy atmosphere, if you're looking for somethning to play on a rainy day. Unfortunately, to my knowledge they haven't been rereleased since the days of the PS3, but the original discs are relatively easy to find if you've the hardware to play them.
Blossom Tales: The Sleeping King and The Minotaur Prince. Independently developed by Castle Pixel, these games, which are also Zelda-inspired, have a much more modern feel. The pixelated graphics harken back to the era of 16-bit, but the controls are buttey smooth and the colors pop crisply. You can find both games on Steam, Here and Here.
Evoland 1&2. Made by Shiro Games, these unique RPGs revolve around the concept of changing graphical styles as the game goes on. The first installment is quite bare-bones, but both games were collected into a single Legendary Edition on steam, and playing the two back to back is a quite nice experience!
Lunar: Silver Star Story and Eternal Blue. Created by the legendary Game Arts in their prime, these turn-based RPGs are some of the best the original playstation has to offer. They're sadly quite hard to find nowadays, but if you ever get the chance, I can't recommend them enough, their storytelling is on another level.
Portal 1&2. Valve doesn't make many games, but nearly every one they've developed has been completely revolutionary. Both Portal and its sequel are some of the best puzzle platformers ever created, with inspired level design and mechanics, coupled with a hilarious and sometimes chilling story set in the Half Life universe. Both games are available on steam Here and I cannot tell you enough how much you should play them.