We all know about Persona so it doesn't qualify. These are spinoffs few people played or know about but were good to great games.

I'll Start with Front Mission Gunhazard. A side-scrolling Run n Gun ARPG. It looks like many side-scrolling mech games of the era but this is Square so it has RPG elements. ALso a great OST that takes advantage of SNES sound.

EX Troopers. Japan only spinoff of the Lost Planet Series. Lost Planet has now fallen to obscurity itself but it was a modestly popular series on 360/PS3. EX Troopers is a more anime/arcadey take on the series. It plays well with a great OST. Sadly stuck in Japan on PS3/3DS. The good news is there is a fan translation patch. And if you don't want to mess with emulation. The PS3 Physical is usually not that expensive and it's import-friendly meaning it's easy to play not knowing Japanese. Oh and PS3 is region free.

Sadly it's difficult to find good videos on this game. It's just not very well known. But is a blast to play.

Does FFT count? Because it is the best final fantasy game in the entire franchise.

No it's pretty well known and got some sequels.

Dead Space Extraction is a really good little game that does justice to its series and makes good use of the Wii's capabilities.

Medal of Honor Heroes 2 has some of most fun and creative controls of any game I've played.

Silent Hill Shattered Memories is effectively scary and has an interesting system where it psych-profiles the player and changes accordingly.

How about a spin-off from a spin-off?

Might & Magic: Clash of Heroes
This game, which debuted on DS in 2009, is a surprisingly deep and varied turn-based puzzle-RPG hybrid

I don't have a game in mind but this is an interesting question. I really came here to say that Front Mission game looks pretty great - never heard of this game now I want to check it out.

Thronebreaker: The Witcher Tales comes to mind. It's essentially the single player aspect of Gwent. It's a prequel to the first game and is played in an isometric perspective with a full set of choices and consequences and is fully voice acted. CD Projekt didn't spare any expense on this game. The big difference though is that your army is made up of a customizable deck of cards, and so when you go into combat, it basically plays out like Gwent with several differences.

It's a great game that I was not expecting to have a deep story to! But it kind of came and went. I never really hear anyone ever talk about.

Virtua Quest in the Virtua Fighter series. Gamecube-only game. A solid if not flawed Action Adventure game set in the Virtua Fighter universe.

Jack Bros on Virtual Boy. One of the better games on the system. It's a top-down action game starring Jack Frost the Shin Megami Tensei series mascot.

Kirby's Blowout Blast

This was technically the first Kirby 3D game, and I think was essentially a sort of demo/proof of concept for Kirby and the Forgotten Land. It was a puzzle/platform hybrid. The objective was to get to the end of the stage, which was relatively easy. The tricky part was using Kirby's inhale ability to take out as many enemies as possibly in one shot, and as quickly as you could.

It was super fun, and the director of the game went on to make Forgotten Land, which is arguably the best Kirby game, so if you're a fan of that, you ought to check out Blowout Blast... Although sadly I don't think there's a way to legitimately play it since the e-shop is closed.

Monster Hunter Stories series is another example that comes to mind. Best Non-Pokemon games I’ve played, and the spin-off series didn’t really take off. Especially nowhere near the way the mainline series took off!