Several series that made the leap from the 8-bit era to the 16-bit era considerably improved on their originals. Super Metroid, A Link to the Past, and Final Fantasy IV & VI are standout examples, having improved and expanded in such a way compared to their NES predecessors that it's hard to go back and play those originals.
Mario 64 showed how to successfully transition a series from 2D to 3D. Many other series tried to do the same but failed, showing that either A) that series' particular play style just doesn't translate to 3D well if at all, or B) the developers just couldn't figure out how to make the transition a good one.
Castlevania was simultaneously one of the best and worst. Castlevania 64 (one of Konami's few N64 games) was a good example of a series making the jump to 3D and absolutely failing. Meanwhile, Symphony of the Night, released just a few months earlier on the PS1, is widely regarded as the best in the series, and retained the 2D gameplay of the old NES & SNES titles.
And on the bad side, Mega Man X took a huge nose dive with X7 on the PS2. Capcom decided to ditch the 2D gameplay and artstyle from the previous six MMX games, and the result was a complete turkey of a game. For the previous generation, I would have also said Mega Man Legends, but it was beat to market by Mega Man 8 by more than a year. MM8 was a decent game that stuck with the classic 2D formula, while Legends felt like a "Mega Man in name only" game, becoming yet another attempt to translate a 2D series to 3D and losing everything that made the older ones good in the process.