Bronies can get fairly annoying but have calmed down over the years. Dr Who fans and Adventure time fans can still bit a bit of annoyance, especially when expressing their love for the show. Game of Throne fans populate a lot of the internet right now and can go crazy when someone says they don't like/watch GoT. Sherlock fans are always complaining about waiting time or something and Walking Dead fans are always attacking others who don't like the show because of the absence of zombies (you'd think there would be more zombies).
In all, al fanbases can get very annoying and troublesome but simce this is a question directed for my opinion, I will say that Dr Who fans or Wholavins or something are more annoying. They mostly consist of teenage girls who feel the need to show that they are "nerdy" and like the awkward, nerd looking British gentlemen. It all just gets out of hand.
Even though I'm a brony and GoT fan myself, I agree that both fandoms can be kinda annoying. Many bronies like to 'ponify' everything and if you tell a GoT fan you've never seen an episode, they can be all like "WHAAAT? Wow, you are so weird! Start watching it, now!" I also don't really like they Dr Who fandom, so I just try to avoid it.
For me it's certain sci-fi fans particularly Dr Who's fanbase.
Gleeks
I think the Big Bang Theory fanbase can be annoying (well not all of them) because whenever you say you don't like the show they freak out at you and tell you that you don't have a sense of humor. What do you think?