I think there are 3 types of successful 2D to 3D conversion. One where the game undergoes radical changes to the overall experience, but also retains the qualities that made the originals special. The second is where game was orginally attempting to emulate 3D gameplay using 2D methods. The last is where the game plays the same as before, except that the game assets are converted into 3D.
For example, Mario64 and Zelda:OOT are both completely unlike their 2D predecessors. With both those games, 3D offered new possibilities and a new experience.
MarioKart 64 on the other hand doesn't play hugely different to Super MarioKart. Super MarioKart is effectively trying to be a 3D game. I guess it could be argued that no conversion really took place. I guess Outrun would also come under this category to a lesser extent.
The last type is illustrated FF7. From what I've seen/played of it really is a 2D game. You've got 3D models roaming around on a pre-rendered 2D backdrop. Compare FF7 to FF6 and you'll see there isn't a huge amount of difference brought by 3D.
Micro Machines V3 is another good example of the last type. Although the environment and cars are 3D, the game is the same top-down gameplay as before, with a few nice tweaks such as zooming out on long fast straights.