World of JRPG's

My old school favorite, not counting Pokémon, is Monster Rancher. I always liked how raising the monsters worked in those games and battling was its own thing that you did to show off the fruits of your training.

A modern game that I loved was Monster Sanctuary. The battle mechanics are very satisfying. The battles are 3v3 and move quickly. The mechanics make for multiple viable strategies. Every monster has 2-4 skill trees and 3 forms, meaning there is a very high level of customization too. On top of that, it’s a metroidvania, so you have a map to explore and areas you can’t access until you find a monster with the map action to get you through

Shin Megami Tensei is by far my favorite one. Due to its adult theming it has got the best designs in my opinion. It ranges from cool to creepy to plain ugly to a giant penis on a chariot - what's not to love? Monster can and should be merged into stronger ones, which I always prefer over evolutions. In addition, the press turn combat system is one of the best turn based system ever created.

If you like tactical RPGs (SRPGs), theres a spin-off series of SMT for that too called Devil Survivor. Thogether with SMT V, these are a some of my favorite games across genres.

Second up is Dragon Quest Monsters. I adore Toriyamas artstyle (e.g. Dragon Ball) and once again it is based on merging your monsters. However, unlike SMT where you'll be constantly merging, you won't be doing it much here. It's also a lot more grinding, but depending on who you ask that's a plus.

Lastly, there's Jade Cocoon. Honestly I don't remember much about them since they are PS/PS2 games, but I remember them being fun.

Monster Rancher
I'll toss in another vote for Monster Rancher ;) A Pet Raising and Breeding simulator that got it's roots from an earlier 1996 game "Gallop Racer" which was a Horse racing and breeding sim. Monster Rancher replaces Horses with Fantasy monsters, and swaps out Races for Real Time battles.

While the Raising aspect is highly menu driven as you make constant adjustments to your strategies for raising stats, learning new attacks, or doing "side-quests" in the game to unlock even more monsters, the Battle is in real time where you control your monster moving between near and far ranges to use attacks that are unique to those ranges. The attacks themselves also have 2 primary types (Power or Intellect) and 5 sub-types (Heavy, Crit, Wither, Hit, and Special). Using attacks has an associated resource cost (Guts) and your monster's guts regeneration differs based on it's breed (or mixed breed).

Loads of variety of strong looking, silly, or fun monsters to pick and choose from.

• in 2021 the original first two games games were re-released as remasters on Switch, Steam, and iOS as Monster Rancher 1 & 2 DX. with upscaled graphics, some overhaul in the UI, and a lot of QoL features added in, but for the most part still looks and feels like the PSX game, just a lot smoother and zero load times.
• in 2022 a new game exclusive to Switch released asa crossover with Ultraman where you raise Kaiju from that franchise but with Monster Rancher rules.

I really liked Cyber Sleuth when it came to raising Digimon after I found out you could put the Switch in sleep mode and they'd still level up on the farm. Didn't really like battling, especially the bosses that had tons of immunities, inflated stats and could spam annoying moves with several consecutive turns

Dragon Quest Monsters Caravan Heart

I like how it is relatively simple compare to other monster games. The monsters are designed by Akira Toriyama.

Is Monster Hunter too obvious of an answer lol

Ni no Kuni: Wrath of the White Witch. Art style is gorgeous, game is a lot of fun and the familiars are adorable. What else could you ask for?

Megami Tensei games have amazing creature design and combat, unfortunately you're encouraged to constantly trade your monsters in for stronger ones

This won't be a seperate post, but as i said, there is to much info about monster games right now: Kazumasa Habu no longer producer of Digimon games; next Digimon Story game still underway

The art style did take a little getting used to, but I did have a lot of fun with World of Final Fantasy. My only wish was that I really wanted a third party member. Maybe a monster-only stack or something. I feel like ATB needs that to make the magic happen. Story also got shockingly dark, but that's not necessarily a bad thing. Off-topic a bit, but I'm kind of a voice acting nerd and my favorite thing about WoFF is that the English cast is insane. It's practically a who's who of video game voice actors in English, and the localized writing is great, too.

My personal favorite monster collector is still probably Pokémon HG/SS. I'd love to see a trimmed-down Pokémon like that era, before all the feature bloat but still after the new quality-of-life changes and soundtrack style (X/Y's soundtrack was such a breath of fresh air for me). I also really liked Dragon Quest V, though that's more for the game overall than its monster collecting/battling elements.