Annoying tweets
ranting
complaining (esp. when it's about something they have no control over)
any tweets with 3 or more hashtags
especially annoying if they contain hashtags + mentions + link(s), since clients often make the hashtags, mentions, and links different colours than the text
talking almost exclusively about social media (esp. Twitter itself)
"did you know that"-type tweets without citations
compressing words to fit 140 characters, making them all but unreadable (why not just make two tweets?)
quotations from famous people, or famous quotes (usually banal)
the worst is when someone makes the quote and makes it seem like they're the one originating it.
retweeting mentions of you that don't really add any information
example, Acme company, with the Twitter account @acme, retweets how someone loves @acme products? Yeah, so?
"[Place name], I am in you." Oh, no, honey, we don't do that anymore.
What You Might Think That I Consider Annoying, But Actually Like
overheard "OH" tweets
talking about what they just did, esp. if it's something that didn't involve them sitting at a computer
talking about something they're doing, to get on people's radar
asking the Lazyweb for something, but only if they've put it some work into finding the answer themselves, e.g. #reco
self-promotion (why the hell not? How else am I going to know the latest awesome thing you did?)
retweeting your other account (not too bad when done in moderation, and maybe I didn't know about your other account?)
retweeting someone's answer to your question (that's great! Now I know the answer you got to your question!)