Ice for the most part, forces you to change the way you play the game by decreasing acceleration/deceleration and turning. This makes you have to think ahead and attempt to keep your momentum.

Because of this, I think its a really good mechanic when done right (like in mario games). I haven't played all the games in the OP but I have never played an ice level thinking "gee, this ice really makes this level worse"...

just my opinion on the matter.

I personally think the worst gameplay mechanic is automatically regenerating health. Okay, thats a bit of a lie...Regenerating health can be good in a certain type of game, the problem is that most FPS games just seem to follow the trend instead of thinking "does this actually make my game better or would another system be superior?".

Underwater is probably the best though I do agree everyone hates ice.

I hate water more because at least with ice I feel I have some control, but with water your control over the character goes to hell. Every direction around you is a danger zone, so if something is sneaking up behind you, you have no idea.

Not to mention that it always adds the air mechanic... I hate having a timer put on my missions like that. So frustrating.

I remember hating Sonic the Hedgehog 2's water level. I remember it was the second level and you would literally be forced halfway through the level to run through this big underwater section and the platforming was pretty tedious. One mistake and you could very well drown.

Then there's the water levels where you can't even go in the water or you die, Sonic the Hedgehog has water like that as well. Grand Theft Auto 3 did as well...

Not to mention that it completely screws around with your control scheme when you are swimming through water. When you are on the surface in water you can just move in the direction you want, but then you need a seperate button to dive underwater, and another button to swim which you often have to push repeatedly. Sometimes theres the odd game where you have multiple buttons for swimming at different speeds. (I'm looking at you Banjo Tooie with 3 different button mechanisms to swim.)

I don't really hate ice but I do dislike it. Sometimes it can be fun but sometimes it's there only to make things harder in a cheap, annoying way. But only rarely do I feel like it really adds something to the game.

Underwater levels.

Sliding down the ice was pretty fun in Xenoblade.

lol

Holy shit... that's Puppeteer? DAMN!

This.

Also, for a specific mechanic, the stupid "use the Wii remote pointer to "draw" the tracks for "Train-Kirby" to travel on" in Kirby's Epic Yarn. For being such an embarrassingly "easy" game, that part was remarkably frustrating. 

I don't like those ice puzzles where you slide on the ice but you can move only in a single direction, it's so annoying.

Something like this: