Mario 64: It was a gold standard in 3-D gaming for years
Final Fantasy VII: They really used the hell out of their CD-ROM storage and CD-i workstations
Zelda: Zelda to A Link to the Past to Ocarina of Time to Wind Waker/TP (GC), and Zelda: Breath of the Wild: Ocarina was a good start in 3-D, Wind Waker and TP refined it, and BotW gave me the huge Zelda overworld in 3-D I always wanted. Skyward Sword was good, but the motion controls made it rough. But Zelda generally does very well at keeping up with generational jumps.
Metroid: From Metroid to Super Metroid, and from Super Metroid to Metroid Prime. I just wish a few Metroid power-ups had translated better in Prime
MGS from 5th to 6th to 7th gen.
Grand Theft Auto I and II to GTA 3: They went from crude, over-head view games to fully 3-D open world games, and GTA likewise went from cult classic on 5th gen to mega-blockbuster on 6th gen.
Fallout 1 and 2 to Fallout 3/New Vegas: 3 was a bit light on RPG mechanics but great on atmosphere, New Vegas put it all together.
Soul Blade on PS1 to Soulcalibur on Dreamcast: probably the single biggest leap for a fighting game I've ever seen.
Mortal Kombat from SNES/Genesis to PS1/N64: The 5th gen games were so bad they would have killed the series if Midway hadn't redeemed itself somewhat with Deadly Alliance on 6th gen.
Mass Effect: Andromeda pretty much tanked on PS4.
Double Dragon: A hit on NES, complete failure on SNES.
Rare as a whole. In the 5th generation, they were called the best developer in the Western world. In the 6th generation, they were putting out crap like Grabbed By the Ghoulies.
Meh - not spectacular but not exactly smooth transitions
Castlevania: I actually liked the N64 games okay, but they were certainly not on the level of Mario 64
Mega Man: I liked Legends as a Zelda-style adventure, but it didn't translate as well as Mario 64
Bomberman: The 3-D Bomberman games generally weren't too bad (except Act Zero - WTF were they thinking?)
Tomb Raider between PS1 and PS2: I guess the downfall started with TR: TLR on PS1, but the PS2 games sucked.