I gripe excessively about this matter, and I'm not sure what others' opinions are. I'll give you two of my best examples for why to stick to 2D in certain situations.
First and foremost is Fire Emblem. For those who don't know the series, Fire Emblem is a strategic combat game. In the campaign, the player moves it's units in order to complete a mission objective, usually killing a boss. Units can attack each other, starting an animation for the two of them.
Looking at the animations for the DS game Fire Emblem: Shadow Dragon and the Game Boy Advance game Fire Emblem: Rekka no Ken, I see a distinct difference in style, and am personally a fan of the GBA style rather than the DS style.
FE: Shadow Dragon:
FE: Rekka no Ken:
Another example is Pokemon. When Pokemon went from the GBA to the DS, it was rendered in 3D. When I look at the game on the GBA, it looks good and everything looks intentional graphically. When I look at it on the DS, it looks pixellated and awful. The reason isn't because the resolution of the GBA was better, it's because the GBA placed each of its pixels consciously. I don't understand why Nintendo decided to take the game to 3D on the DS even though it would look like this.
In general, my point is that if putting the game in 3D doesn't add anything to the graphical style of the game (or worse, takes something away), then it isn't a good thing.
Anyway, this is my take on this situation, and I'd like to hear yours!