The game mechanic I hate the most would be...
Random Chances - "Hey, I've got an idea! Let's have an attack/event rely completely on luck and throw any sort of skill or effort on the player's part out the window!" I hate random chances, even when they work in my favour. Once I played X-Men Legends and was low on health. I got hit by an attack that should have killed me, but didn't because my character magically blocked the attack without any input from me. I just love it when my character is doing the playing for me.
It's ridiculous how in many action RPG's you have to level up "dexterity" so that your character has a higher "chance to hit". You see your character's weapon clearly connecting with the enemy's body, but absolutely no damage is done.
Grinding - Kill the same weak monster over 9000 times so that you can level up and kill slightly stronger monsters an even higher amount of times. It wasn't fun or challenging the first 100 times, and it's not showing any signs of improvement anytime soon.
Enemies that don't stagger when hit - It's really annoying when an enemy can smack you whilst having your boot embedded in his face. The only time when this is acceptable is when you're fighting a big slow giant.
Turn-Based RPG combat in general - (Fighting normal enemies: attack - attack - attack -attack -attack - win) (Fighting bosses - boost party - attack - heal when necessary - win if your characters/items are strong enough, otherwise you're screwed) Kudos to Paper Mario and Grandia 2 for having combat systems that are actually GOOD
Puzzle-Based Boss Fights - Someone else brought this up and I agree with them wholeheartedly. First of all, the only kind of challenge is finding out the boss' weakness. After that, all the fun goes out the window, especially when you have no choice to stun an enemy using an item that's otherwise completely worthless in a fight (Morph Ball Bombs, I'm looking at you), and then proceed to mash the A button repeatedly until the boss recovers. What I hate about it most is that you're FORCED to use certain weapons without any exceptions. What's the point in giving me all these cool weapons when I'm forced to use 1 or 2 of them throughout the entire fight?
Long Travel Times - I love sandwiches and all (points to username), but if I wanted to go make myself one I would pause the game, or shut it off.
Button-Mashy combat - It really kills the fun when the most effective way to defeat enemies is to simply stand next to them and tap the "A" button until they die, or launching fireball after fireball after fireball, with a little bit of running away to spice things up. No maneuvering or skill necessary.
Not exactly a game mechanic, but I really hate short, easy, no replay-value at all games. They might be okay for a rental, but they're a complete waste of money when it comes to buying.