I think TR: Chronicles is when things really started to dip, but the drop to Angel of Darkness was quite something. Legend and [iAnniversary were pretty good though.

BoF6 made me sad. Looks like Maple Story. I really enjoyed 3 and 4. Never played Dragon Quarter.

Halo. What an amazing reimagining of the Atari 2600 Classic.

As others said Metroid has to be among the best: There were countless scenarios where making the jump in 3D could've resulted horribly but they pulled it off

Buuuut, Halo to Halo 2 didn't involve a generational transition. I do agree that Combat Evolved was superior to Halo 2 ( at least if we're talking the main campaign ),  but would stop well short of saying it wasn't anywhere close to being as memorable.

Worst probably goes to socom for me. The PS3 hit and that series just died. Also crash and Spyro from ps1 to ps2.

Best is ratchet from PS2 to 3 because I didn’t think they could top UYA but ACiT is my favorite game ever and ToD was the reason I bought a PS3 and it was awesome

As usual, Castlevania takes a hit, but really wasn't that bad...it just couldn't live up to Nintendo's 3D entries. The whole transition to 3D could be seen as problematic, Metroid and GTA are probably the only series that actually improved in sales (maybe Zelda)? Super Mario 64 was a good game, but jdging by sales, @The_Liquid_Laser is not the only one who disliked it.

I personally found the GameCube gen was lacking for Nintendo. Super Mario Sunshine, Wind Waker, Paper Mario: TTYD, all left me cold compared to their N64 counterparts, and I was really feeling the loss of Rare. Not saying any single one was terrible (in fact for a long time Wind Waker was my favourite even though I recognized it was very flawed) but the ongoing let downs added up to drain my enthusiasm.

Best:

Mario most gens. The new games may not necessarily be better than the older ones, but they almost always take advantage of the new hardware in a great way.

Zelda most gens as well. But I don't count BOTW because it is also on the Wii U.

Metroid. Super, Prime 1, and Prime 3 are all fantastic showcases for their systems.

Smash. Each new game is a great expansion on the last with new modes and great new additions to the cast.

Final Fantasy until the HD era.

MGS.

Worst

DK64. Went to far.

Banjo Kazooie nuts and bolts

COD Ghosts

And the absolute worst is Mobile Suit Gundam Crosswire for the PS3.

Zelda SNES to Ocarina -> That was brilliant.
Mario SNES to 64 -> bad, the last great mario for me is World.
64 to Sunshine -> even worse than the one before, killed Mario entirely for me.
Sunshine to Galaxy -> very good
Zelda TP to SS -> ghastly, worse leap I've ever seen in the history of video games. Zelda SS is the worst AAA game I've ever played. Worst Zelda ever, worst Nintendo game ever, one of the worst video games ever made in the history of the solar system, aliens will mock humanity forever because of this game
FF SNES to VII -> brilliant
SFIII to Alpha/Alpha2 -> great
Super Metroid to Prime -> spectacular, that's the only Metroid i can handle playing
MGS from whatever to whatever -> great
GTAI and II to 3 and the others to their next -> great

Now, best and worst


WORST:
Zelda TP to SS -> a brilliant game to the worst zelda

BEST:
God of War III to God of War PS4 -> universal acclaim to one of the best games ever made

Good ones: Mario, Zelda, final fantasy and metal gear switching to 3d
Bad ones: basically everything else switching to 3d.

Looking back to a lot of those n64 ps1 era games it's probably for the best Metroid and fallout waited