For me, Banjo Kazooie, Banjo Tooie and Donkey Kong 64 come damn close.  Conker was great too.  The N64 was a 3-D platform lover's wet dream.

Metroid.

Final Fantasy.

Mario > Zelda > Metroid

GTA and Mario are my favorite choices. I still remember being blown away playing Mario 64 for the first time.

On the flipside I wasn't a fan of DK's jump to 3D. I loved the DKC games on SNES but DK64 just wasn't as fun and I haven't enjoyed a DK game as much since.

Final Fantasy is high on the list (FF6->FF10).
Metroid is high on the list, probably more in terms of gameplay than FF.
Mario is probably the highest on the list in terms of gameplay, but not as much graphically.

Pick your poison.

Zelda, followed by Metroid, and then Mario. Can we count F-Zero, also?

Metal Gear Solid, while fantastic, was great for it's mood and themes, but I felt the gameplay wasn't really what I wanted out of it. Played through it twice, but each of those other franchises I mentioned, I've played through many, many times, and through many titles.

And Gling Gling, why would mario not be up there as much, graphically? When the N64 hit, there wasn't anything that compared to Mario, Sunshine was gorgeous, and Galaxy is one of the best looking Wii games to date.

Though I must say I await to have to change my opinion with the upcoming showing of Kid Icarus.

It all depends on what you mean. If you mean retaining the spirit of the original gameplay while transmuting the medium to the third dimension, then I think Mario pretty much has that one nailed; all of the 3D entries play and feel like faithful 3D adaptations of a 2D system.

In terms of changing the gameplay best to suit it for 3D, I'd say that Metroid had the biggest task cut out for it, and did the most impressive job of remaking itself for a medium that it was never really intended for. Say what you like about Zelda being well-adapted, but it was a series that lent itself to 3D far more than a side-scrolling exploration-based game like Metroid.

For the improvement of visual style between the 2D and 3D spectrum, Dragon Quest definitely takes the crown (well, DQ8 onwards anyway; we'll forget that DQ7 is technically 3D). The realization of DQ artwork in 3D was no small task, and Level-5 did an amazing job of it.

As for the series least impacted by the transition, Final Fantasy comes to mind. It took until FFX for the games to even get full 3D environments (at which point they ended up losing detail in favor of being larger), and though the battles have been in 3D since FF7, they still all play out like their 2D counterparts, with the addition of spastic camera work to help induce nausea in more queasy players. I've nothing against the series, but I can't help but feel that Square-Enix has made the least impressive effort of all companies listed in this post thus far to really make the most of 3D over 2D.

Well, Mario, Zelda and Metroid. Definitely. All are perfect examples of how a 2D-to-3D transition should be done. Flawless.