It really depends on how and why you consider a Pokemon annoying.
As far as the games are concerned, Tentacool and Zubat always annoyed because of how often they showed up in water/caves, and Roggenrola annoys me because not only is it an all-around boring and uninspired Pokemon, but it has Sturdy, which means I can't OHKO it. For the series in general, Pikachu mildly annoys me. I understand that it's the franchise mascot, but I wish more that other Pokemon could be used to market the franchise, too.