The most annoying conspiracy theories are creationism and that global warming is not real, because they are so potentially damaging for the human race, although I appreciate many would not class them as traditional conspiracy theories like 9/11.
Conspiracy theories don't annoy me so much, although they are often disrespectful to the dead. The attitude of certain theorists is quite annoying, especially the type that obviously spend a lot of time on certain 'truther' forums and say everything is a conspiracy, and spout ill informed paranoid nonsense or made up science about subjects that have no actual knowledge or experience of. The ones that frequently shout 'wake up' and call anyone who doesn't conform to their alternative but narrow ideas a sheep. They can be pretty annoying and I generally try and avoid them. What these people don't realise, other than how hypocritical they are and get very upset when challenged, is that if you spend time in these online echo chambers and actively seek out theories like a hobby, wanting them to be true, their judgment is clouded. They can't look at anything subjectivity and cherry pick, so the theory which may have some truth, loses any credibility. It's so obvious they subscribe to a theory because they simply like it, not because it's likely to be true. I guess some people also feel empowered by them, as I see people frequently use them to justify the problems with their life, which is often due to the bad decisions they have made, by blaming the authorities etc.
It surprises me how gullible people are on social media too. Never ceases to amaze me how someone with a rudimentary understanding of Facebook can create the a obviously made up meme and people repost it like it's an indisputable fact.