Oh man I came into this topic pretty scared because I didn't wanna have my comic display some awful tropes. After reading through this whole thing, I realized that none of the characters I have created for my comic GLITCH display most of these tropes lol. I have my characters in high school though, just because that's the target demo for these kinds of things. But this is an "American" highschool so there won't be any Japanese high school anime tropes.
I have the childhood friend trope, but they are NOT in love. They are literally like brother and sister, and care for each other, but that's it.
Basically I'm not including tropes that I hate, which are:
Harems
Tacked on romance: Not EVERY anime needs romance. It just gets in the way.
Dumb/clueless main character: I don't HATE this trope, but its overused. I still like some manga/anime that use it though like One Piece.
Moeblob characters
Tsundere characters
Having the main character constantly beat up by his female friend for comic relief: I REALLY REALLY hate this
Deus Ex Machina: I don't hate this too much, it works sometimes, but I try to avoid it.
Power of Friendship trumping all!: Again, not something I hate, but I think its overused. Sometimes a character should just be defeated.
Freaking out during sexual situations: This gets used too much for comical reasons, but its just the same thing every single time and its pointless and stupid.
the deadpan "emotionless" character: Just... ugh..
Those are just a few, anyway.
People need to start taking these tropes, and turning them on their heads and trying something new with them. Manga like Medaka Box does this well, it makes fun of a lot of shonen tropes and exaggerates them. Its a really great meta manga, give it a read if you haven't already. Just make sure you go in knowing that everything it does is making fun of shonen tropes, don't take it seriously.