The logical fallacy I encounter the most that annoys me is the straw man. For clarity, a straw man argument is when instead of attacking an argument put forward by your opponent, you attack a different argument which is easier to defeat. The most recent example is when debating abortion, somebody tried to present my position as... I believe it was the Lockean position on personhood, where individuals don't become people until they gain some ability to make moral positions, and then arguing from there that by supporting abortion I was arguing that it should be ok to kill young living children. I was making no such argument (additionally, he was using the Lockean argument out of context).
Straw men are also commonly linked to false dichotomies (presenting a scenario as binary when it is not). In the above mentioned argument, it took me half an hour to get my opponent to admit that he was not only presenting a straw man, but also creating a false dichotomy, in that the only valid opposing position to his theory was Lockean. Another example that was in the Canadian news in recent months was that one of the Conservative cabinet ministers (Vic Towes from Manitoba) introduced an internet surveillance bill, and argued, in Parliament, and to the national media, that if you opposed the bill, it was because you were a supporter of pedophiles, when in fact that there were many reasons that people could be opposed to the bill, such as the fact that it violated charter rights.
Straw men are also commonly linked to false dichotomies (presenting a scenario as binary when it is not). In the above mentioned argument, it took me half an hour to get my opponent to admit that he was not only presenting a straw man, but also creating a false dichotomy, in that the only valid opposing position to his theory was Lockean. Another example that was in the Canadian news in recent months was that one of the Conservative cabinet ministers (Vic Towes from Manitoba) introduced an internet surveillance bill, and argued, in Parliament, and to the national media, that if you opposed the bill, it was because you were a supporter of pedophiles, when in fact that there were many reasons that people could be opposed to the bill, such as the fact that it violated charter rights.