Besides some points from both Zinga and Assassinator,

let me think what all I hate.... (and maybe rephrase some other points):

Character who are only good for "What do I do?!!!" or " Um... er.. {freaks out}" for about 90% of the anime. A case study example would be Orihime from Bleach.
How the lead boys are surrounded by girls with considerable sex appeal and NO OTHER guy ever talks to these girls and how none these girls EVER talk to or about any other guy and how they ALL cherish a love for him. (And as Assassinator said, he's totally oblivious to that).
The concept of the Hero with a stone can beat the bad guy with a deathstar (from the planet).
No one ever feels the damn coldness of the snow (not only during action).
The bad boss always have at least one henchman who is only in it to find the strongest possible opponent by whose hand he can die (usually the main character) and that this henchman is cold, ruthless and insanely powerful. And yet the hero will beat him and cause a change in his character as he dies, turning him into a good guy.)
All dying people seem to have a flashback which involves a lot of black and overlapping layers of images.
How the females characters are all mostly overly well endowed and wear clothing which must have titanium strings keeping them from being torn of from certain areas.
The above mentioned females don't seem to notice this condition or their sizes till someone points it out to them.
There is always a secret plot or a ability to unlock. It usually always involves some sort of trauma.

there are more... can't think of any right now though..