I have seen and experienced many but what annoys me the most is when they say they did something without explaining what they did, how they did and how they managed to Dynasty Warriors 1000's of enemies without breaking a sweat. Normally it is a giant explosion that somehow leaves them unharmed or somehow a magic shield protects them because suddenly they are the chosen one. Even worse then that is one they one line it and cram it together hoping it is makes sense and is acceptable. Surviving something that can kill you is OK if you explain how and do it right but when done in an OP way I am like nope.

I think I remember one where the enemies out weighted the two main characters and the partner decided his character was Goku all of a sudden, before I know it his power level is over 9000 and I am like what is going on. Suddenly the other character is half an angel and half a god and it was not until this point they awoke to this. Basically things die and they write it off like it is nothing, I added more and more waves hoping they would knock it off but sadly it did not. 

Another.

I remember my very first group RP, it was a gang based RP which had many gangs and also had a FBI faction as well. At first the cops were normal but half way through of sorting a map to see what gang controlled what area things went to shit. Suddenly I was the target, I was a crazy guy in a bear suit who led a gang of insane and crazy people. I had a lot of logically escape plans but somehow the police and FBI suddenly knew where I was going, what I was doing and basically controlled what I did the whole time until the breaking point happened. Basically everyone got annoyed with the FBI and started arguing and after that started to post stupid shit and within the space of 2 hours the RP was destroyed.

I have made RP's where one becomes broken but I explain how and why and usually add some negative effect to it such as becoming comatose, dying afterwards, going insane to the point they are no longer able to function without help aka needs to be locked up or whatever else I had come up with at the time. It is thought out and sometimes really thought out as well.

I do have a villain who is broken but he is not unbeatable, he is my general villain who I don't really get to use much. He is kind of like Thanos and Ultron. Thanos in terms of him needing to be gang banged or trapped in someway and Ultron in a way he keeps coming back no matter how hard you try to remove his presence. I have never written something like he blocks all attacks and strikes them all with an unblockable and swift counter. I always give chances for RPer's to counter them back though if it is for the story I may force it upon them, though it is not like I am killing them or anything.

Basically if someone just undermines everything you throw at them then you have a OP character, even worse when they know they are doing it but won't stop or write it in a very crap way. Oh when they agrue they are not broken also gets on my nerves where they won't leave and think it is cool just to write a post about how they killed or dominated everyone and everything.