Timers, or in the case of platformers auto scrolling levels. I like to explore and not be rushed. Leave that for time attack mode. Why does Mario have a level timer? What purpose can it possibly have but to annoy you?

Second worst is not necessarily a gameplay mechanic, it's that invisible line you cross triggering a mini cutscene closing off the level behind you. Make it clear when you're about to step into the next section.

Long standing annoyance is context sensitive buttons. For example why are dash (roll) and ground pound mapped to x+y on the gamepad in donkey kong. Why can't it be separate buttons. It happens too often I try to sprint out of the way and he stands there pounding the ground instead. Grab and run on the same button is irritating as well in co-op, we keep picking each other up by accident.

Timed segments in RPGs. Its okay for a boss fight (think emerald weapon) but training escape where before whatever terrible thing happens while spawning random encounters sucks.

Auto-scrolling.

random encounters

I hated the underwater levels in Banjo, the Mario 64's ones were better.

The combination of random encounters and having no map when you are in a comlex dungeon... just annoying if you try to figure out where to go and you get attacked every 5 steps...

Motion/Touch control mini games that are tacked on to games... My worst experience was AC Liberation on the Vita: I couldn't open that letter because my Vita did not recognize my sliding on the front and the back screen. Or the sequence where you had to hold the Vita against some source of light to be able to read the secret ink letters. I was riding on a train to Vienna and I couldn't find a light source strong enough and this minigame was unskipable.

Or some Wii Games like Silent Hill... If you wanted to open a door or a drawer you had to aim at it, hold down the trigger and make some movement... What where the developers expecting? Should I get excited that I opened a simple door? What an achievement...

Online-Multiplayer: Ok, there are games that were made for this. But why do I have to cope with it in almost every game... Tomb Raider, God of War, Assassin's Creed,... I don't like it and it feels like playing the same old game again and again and again.

Escort Missions: Just an example: I am just playing Tactics Ogre on my PSP. There was a mission where you had to help a certain character. At the start of the battle she was located next to the enemies, outnumbered. You had to rush to her so you were able to heal her. And what was she doing? Escaping? Trying to reach a healer? No, she was attacking, even as her HP got low. Very intelligent.

Dark rooms: Sometimes the screens turn dark and you have to reach the next source of light within a certain time.

Unbeatable fights: In some RPGs you have to fight an enemy that you simply can't win. It would be nice if you would know before, so you don't spend a long time trying to stay alive and wasting your precious healing items.

Decision trees/good or bad: I hate permanently missable things in games. I prefer one long playthrough where you can get 100%. Playing a game over and over to be able to see every possible ending is something I dislike. Heavy Rain was a great game, but replaying it over and over... Beyond Two Souls was the same thing. I somehow liked InFamous but the second Playthrough was soo repetitive. This gameplay mechanic alone made me lost my interest for this franchise.

Final Fantasy VIII, enemies increasing their levels when you do, and they improve more than your characters. That makes leveling up (and battling) pointless. In fact, the game is easier if you run away from everything to stay at low levels. Either that or drawing magic.

Auto-Healing. I want my healthbar!

Took me a bit to get used to it but I loved the ice skating in Mario Galaxy, and the ease of transition between walking (slipping) and skating.
In general though I agree. The mini-dungeon in OoT to get the iron boots was a particularly annoying example.

That and their speed is usually slower then yours so you have to constantly stop to stay with them.