High pitched kawaiiko female voices. It's annoying and creepy. In fact, I find the whole kawaii craze offensive.
Dumb-ass male protagonists who can't read signals but some how gain the attention of beautiful girls. It's just frustrating to watch them be so pathetic.
Unnecessary vocalizations. I suppose they do this because they have no confidence in the ability to portray body language. Take a shot of vodka every time someone makes a sound with their mouths that isn't a word or some Japanese grammer/ courtesy thing. You will get drunk. Fast.
The hair. It's just ridiculous sometimes.
Bishonens. Translation: guys who look like girls. Considering the appearance of J-pop celebs, I wonder if Japanese girls are all closet lesbians.
Shippers, though that goes for pretty much anything. I have my preferred couple, but it doesn't keep me up at night.
Yaoi Fangirls. I will hunt down every last one that dares to sully the name and dignity of my favorite characters with terrible fanfic-porn.
Leary, leary bad Engrish.
Long Runners. Aside from Naruto and Bleach, and I'm only reading the latter to see it through to the end (or Tite Kubo's mental breakdown, whichever comes first) I refuse to watch/ read anything that hasn't already resolved. If I wanted to spend years thinking "What's going to happen next?" I'd watch a Soap Opera.
In Shonen:
The fiery, protagonist who's a dimwit, though extremely talented despite constant reminders from others that he sucks.
Big F*cking Swords. Or BFS for short.
When characters explain the nature of there technique to their opponents before it is even applied. Doubly so when the technique isn't a straight forward attack and more akin to a standard status ailment that can be avoided by knowing how it works.
On that note, Calling Your Attacks (not linked to TvTropes for the sake of your sanity). Unless saying the name is pivotal to it's use, it's just jarring. I'd like to see someone punched in the face for their troubles, just once.
Super speed. I know it's like a staple of the genre, but it gets really boring. It's almost as if the mangaka (sp?) couldn't be bothered to have anything that actually looked like martial technique, so decided to, essentially, draw two trains crash into one another till they broke. And then you run into all sorts of plot holes that could be solved with super speed if the characters didn't have selective amnesia.
Flurry Attacks. When someone gets punched or slashed at several dozen times all at once. There's a reason why a fight between two people who know what they're doing is really short: You can only fight for so long before you lose focus and fail to safely counter. Then you die or are unable to continue fighting. Rurouni Kenshin is probably the only show that made it awesome, and even then it was only eight or nine hits and there were never any endless flurries were they just stand there and wave their swords around.
Fights that last forever.
Female characters that inevitably and up on the sidelines and are useless in every way except for in kidnapping plots and fan service. They don't have to be action girls, but there's plenty of room between Action Girl and doormat.
No team work. Characters seem to be content just standing around and watching their friends get slaughtered.
When comic relief comes about in an otherwise dramatic moment. The impending disaster always waits patiently while the characters do or say something "humorous". Bleach is the greatest offender.