Mary Sues - Anime's and a great deal of japanese writing has a clear obsession with them. While it's obvious to why these characters are so appealing, they more or less get by on their haxed writing and often don't suffer enough character development to properly change.
Biggest offenders to this are, Sasuke Uchiha (get's a pass because he's the primary rival character), Ichigo Kurosaki (he's every single character type under the fricken rainbow), and Kira Yamato from Gundam Seed Destiny (Gundam Seed wasn't as bad, but his plot armor moments contribute greatly to his Ultimate Coordinator BS status and his completely stagnant character development in Destiny).
Plot Armor - Something under the context of their own universe and set rules being completely subverted because of main character, or popular character prologic bullshit. Example, again Gundam SEED Destiny characters Neo Roranoke, and Kira Yamato surving a nuclear holocaust at point blank range.
Left field pairings - Pairings that simply come out of no where to simply subvert away from the more obvious one for the sake of that. Setsuna X Feldt from Gundam 00 is the best example. These two characters don't interact nor develop enough to invest into a solid relationship to establish a pairing. It's like saying Naruto x Ino is a possibility because ******** it less obvious than NaruHina or NaruSaku.
Extremely obvious pairings - Pairings that exist because of how much it is showcased and broadcast through openings, endings, and god knows what else. It's not so much that the more obvious characters are forming a relationship as much as the series overall emphasis on it when more serious events are happening. Pairing obsession overall is one of if not the most annoying cliche for a non pairing heavy based anime. EX again Gundam SEED Destiny, most of it, if not a great deal of key characters are in pairings and the series excessively focus on who's with who rather than other important things like plot and character development.
Main protagonist sitting by classroom windows - It's seriously an extremely overdone cliche.
School rooftop - An equally overdone cliche.
Harem no jutsu logic - series like these obviously exist for hentai fodder and really nothing else since it's really the same rhetoric over and over and over again. If the guy if not falls for the first female character, he'll remain completely oblivious to his other options throughout the majority of the series, it's only investment is the pairings that really are NEVER going to happen.
Dere's - Especially the Tsundere a great deal of these characters vary, but it's an overall repetitive formula and the Tsundere character can obvious create the most unlikeable female characters I've ever seen in fiction.
The civilian mecha pilot trope - Because immediately it follows mary sue logic and honestly it's been excessively done to death and ignores a great deal of logic. Originally given the superior performance of the character's machine, the said civilian pilot quickly and eventually completely surpass all ace pilots in amount short time. Gundam often contributes it to their next level super-human BS, but other mecha overall generally does this trope to death.
Moe style animation - Said put I find very little variance and work into these character designs and I find the overall concept fairly lazy when the concept is overall the same with very little variation.