Dino Crisis. The first 2 were fun on PS1, but then DC3 was complete garbage and went exclusively to Xbox.

This franchise needs to come back! If MS wants to get exclusivity for it again Im all for it and will buy an XB Series S if they revive this and it doesn't look like garbage.

Colony Wars - Weirdly, now would be a great time for Sony to revive the series, what we VR and all.

Wait, didn't have a PS2 game... :P

For me:

Bloody Roar

X-men/Marvel Legends 

And Mass Effect obviously.

Megaman!

8-bit era: Awesomeness
16-bit era: Awesomness (well personally I actually preferred NES Megaman, but Megaman X wasn't bad and is probably considered better by most people)

Then CRAP after CRAP after CRAP (remember playing some Nintendo DS Megaman game that was so lack luster).

To be fair it found it's way again with with Megaman 9 and Megaman 10 (I can't judge 11 since I've not played it), but it has a lot to do with it going back to it's 8-bit glory.

Here are some that I don't think were mentioned yet.

"New" Super Mario Bros. - great on the Wii, but meh on the Wii U.
Wii Sports Club - The biggest franchise from Gen 7 becomes digital only games.  Really felt Nintendo was trying to kill off Wii Sports.
Tetris - The first game was basically perfect as is.  Every iteration after it had this "what the?" effect.  Now I love Puyo Puyo Tetris, but it took them 5 generations of tries, before one of their spinoffs actually was better than just plain old Tetris.
Katamari Damacy - The PS2 games are great, but the later games were disappointing.

Kingdom Hearts and Team ICO - These fall into a special category in that they started great on the PS2, were totally nonexistant on the PS3, and then were disappointing on the PS4.

Legends is awesome.

I know not quite the same thing, but Quake. The first 3 would've been from that same generation but after that, really went downhill! At least for me, personally.

Fallout dropped from New Vegas to Fallout 4. The settlements in 4 were an interesting twist, but everything else about Fallout 4 was a steep drop from New Vegas. Then Bethesda dropped the series off a cliff with Fallout 76. Even with 4 being worse than NV, that's one hell of a decline within the same generation.

Mortal Kombat from the SNES/Genesis to the PS1. Arguably Street Fighter also declined during the PS1 era.

Final Fantasy from 12 to 13. 12 was awesome in spite of a troubled development cycle. 13 collapsed under the weight of its own hype, and Square Enix in general was flailing the whole generation. And when 14 released later the same year in the condition it was in, it didn't look good for Final Fantasy. It's amazing they were able to do such a turnaround with A Realm Reborn.

Dragon Age. Oh, yeah, I'm going there. 2 had its faults, but in retrospect, Inquisition was the starting point for everything that went horribly, horribly wrong with MA: Andromeda.

Disagree. SEGA made the best F-Zero game in GX. I'd love for them to make another. Most of that core group is still together making Yakuza games.