There are plenty of games that I can list that I know most people are going to recommend anyways, so instead I want to focus on a few gems that I personally love from the bottom of my heart.
The first is Klonoa: Door to Phantomile. This is a charming 2.5D platformer by Namco with an amazing soundtrack. The whole game is centred around grabbing and throwing enemies. You can throw them in front of you, towards the background, towards the foreground, or you can throw them straight down to get an additional height on your jump. It also has one of the most memorable endings to any video game that I have ever played. It's a game that sticks with you long after it's over.
Next is Brave Fencer Musashi. This is a top-down action RPG with platforming elements. It's often compared to The Legend of Zelda, but there's a lot more depth to it than your typical top-down Zelda game. You can copy enemy abilities to solve puzzles or to expand your combat options. It's a PS1 game made by Squaresoft, so you know the production value is going to be pretty high for this one. And yes, the soundtrack on this one is also amazing.
Finally, there's Bubsy 3D. An absolute masterclass of 3D game design that was underappreciated in its day.
Nah, I'm just kidding. My final pick is actually Mega Man Legends. I love this game too much not to recommend it. Most people prefer its sequel, which I also recommend, but this one has a lot of love behind it. This is one of those games that you can blast through pretty quick, but the real heart of the game is the sidequests. Everything in the game revolves around this one town on an island, and every person in town has their own story and personality. Helping out townsfolk and getting intertwined in their stories is what makes the game for me. Even if you're not into sidequests, the main plot is no slouch. It has an intriging mystery that strings you along over the course of the game. It's not a complicated plot, but it's elevated by a cast of extremely likeable characters. Of course, since it's a Mega Man game there's a lot of shooting robots. You mainly do this while exploring a vast tunnel system below the town. It's fun mapping the underground tunnels to see what's behind the next corner. This game is a must-have.