Something that irritates me more than anything is people who cut me off in the middle of a sentence to start talking. Or, anyone getting cut off mid-sentence annoys me to be honest. It's so rude to do that. Sure, you might be anxious to say something their story reminded you of. Or you might be bored with what they're saying and want to change the subject. Or maybe you're just self-absorbed and care more about everything you have to say over ever listening to anyone else. I'm sure there are a lot more reasons it's done and most of them just break down into the person cutting in being a rude douche.
I know several people who do this quite often and it irritates me. Then when/if I cut them off to inform them I wasn't done, I'm the rude one some how. Or, if I don't cut them off so I can finish what I was saying, I just keep going as I was and raise my voice to talk over them. Which is also rude, apparently. However, neither is as rude as someone who always jumps in mid-sentence because what they have to say is obviously going to be wiser, more funny, more important or better in some way.
That's my .02 on the subject. :)