Ratchet Gladiator / Deadlocked.

Yes it's very different from the others but it's still a great game in it's own right. Playing through the whole game in co-op is great.

I like Phantasy Star III just as well as PS II.
For the first I have personal nostalgia so I can't be objective about it and PS IV is the great finale of the series, so those two are above II and III. But I still think PS III is hugely underrated and deserves its place in the quartet just as much as PS II.

Pokémon Brilliant Diamond/Shining Pearl are bad remakes but as games, I find them very enjoyable. I mean, it's Diamond/Pearl without the requirement of using HMs on your Pokémon, making traveling through Sinnoh, which is a fantastic region, is way more pleasent. Don't get me wrong, I still prefer Platinum over BDSP but, the truth is that I prefered playing my Shining Pearl to play any other Pokémon game on the Switch, including Pokémon Legends Arceus (haven't played ZA yet)

Banjo-Kazooie: Nuts & Bolts.

It doesn't reach the insane highs of Banjo-Kazooie or Tooie, but it's a great game. The art direction, music, and environments are impressive, and the vehicle editor is a revelation; it's essentially a game in itself. Moreover, the game strongly encourages experimentation and offers the player an obscene amount of freedom to solve problems. And all this is set against that lovable self-deprecating Rare humor.

Super Mario Bros. 2 is the obvious one. It's really not a Mario game at all, but it's not to bad when given a chance. Tales of Symphonia 2 got roasted and it should have it wasn't as good as Tales of Symphonia which was one of my favorite jrpg's of all time. But you know what, it brings back all of my favorite characters from the first game so it's still a good game even with the annoying main character.

Castlevania Lords of Shadow

I dunno if its still considered a "back sheep" but back then it didnt have a good reception in the community due to the unoriginal gameplay it had and a lot people were on the fence with it. Yet, the game is so enjoyable, story is great and the gameplay that everyone criticized at first fit so very well. It easily became one of the very best Castlevanias for me.

Sadly the sequel sucked balls.

Metroid:Other M

This game got shunned en masse for its portrayal of Samus' "daddy" issues and her overall mental weakness.  While I admit that I am not a big fan of Other M's cringy story and cut scenes, the game itself was fantastic, imo.  I enjoyed the level design and puzzles and blasting through the morph ball tunnels was a lot of fun.

FF12. The story and gambit system are actually pretty great.

It kept the battles fresh for me by continually fine tuning the gambits, basically programming AI for the group to handle fights on their own with no or minimal intervention. And making easy switches for different scenarios. It looked great as well, one of the last games where pre-rendered FMV felt like a reward instead of in game cut scenes you can't skip fast enough.

Of course then FF13 became the black sheep with it's completely on rails linear start. That still had a great chapter 13, but not as good as FF12.

Actually FF only kept getting worse, but FF12 was great!

Glad this was the first response - it was what immediately came to mind upon seeing the topic. Definitely agree about the movement. I do see people critical of the handling in this game sometimes, but I think it's good. Also appreciate the detail they put into making it feel like a cohesive world (e.g. the way other levels are visible from the level you're currently in).

Super Mario Bros. 2 (USA) for sure.

At the time I had no idea it wasn't originally designed as a Mario game, I just knew I was having fun. And it introduced characters into the Mario universe like Bob-ombs and Shy Guys that we may not have otherwise. I actually ordered this game by catalogue and managed to receive it before our stores actually had it and I'll remember the day I came home from school and saw it sitting on my NES forever. Good times.

I can only imagine the disappointment I would have had if the "real" SMB2 was what I experienced as Mario 2.