Pokémon! Surprised nobody's mentioned this really...Anybody hear of Ni No Kuni? It's sorta like Pokémon. Never played it myself but I watched a youtuber play it. Beautiful game.
Monster Hunter Stories. I was so excited about the game when I first saw the Japanese trailer back in 2015 (AKA when I was most into MonHun), and after playing through it (I finished playing it last Sunday), I can safely say that t's my favorite non-Pokémon Pokémon game as I'll call it. There's also SMT4 but I haven't finished that game yet. (In other news, so excited for SMT5!!!!!)
Don't really think I have a favorite game that's like pokémon but I suppose Digimon World is kinda like Pokémon and I really did enjoy playing it back when PS1 was still a thing. Monster Hunter Stories too even if I still need to actually finish that game.