All kinds annoy me, but probably the one that I find particularly irksome is the 'I'm not bias...' or any variant. People use it all the time to try and make their point seem better than it actually is. What particularly gets me is it is inherently false. Humans can't escape bias. You can combat it and minimize it, but you can't get rid of it. In fact, the mere fact that you made a choice or conclusion on something is itself a bias.
Another I've seen several times is the argument 'it's a slippery slope' not used to critic an argument, but the argument itself. I just find it silly as they are pointing out their own logical flaw without even realizing it. Fortunately, I've only seen this a few times, but always gets me laughing when they do.
Edit:
Oh, one other thing I've been noticing a lot lately is a weird variant of Straw man. This is where person X makes a pretty straight straw man position, then person Y steps into the argument on the other side, but instead of disputing the straw man, goes right along for the ride. Person X is bad enough, but person Y... you're terrible. Either you believe the straw man position and thus are a nut job, or you are just foolish and muddying up the waters of the debate for the rest of your side by making your side by looking like a bunch of nut jobs. Please be very careful stepping into a debate on one side to know your actual side.