1. Straw man – an argument based on misrepresentation of an opponent's position. These are as common as crows.
2. Non sequitur. The most popular anarchist non sequitur is: Capitalism is in crisis, so it is about to bite the dust.
3. Reductio ad Hitlerum (playing the Nazi card) – comparing an opponent or their argument to Hitler or Nazism in an attempt to associate a position with one that is universally reviled (See also – Godwin's law).
4. Appeal to novelty (argumentum ad novitam) – where a proposal is claimed to be superior or better solely because it is new or modern. e.g. anarcho-syndicalism is stupid because it is old, egoism is an anachronism, the black bloc is an anachronism best left to the dustbin of the late 90s and early 00s (!). Especially popular among hipster anarchists who decide what ideas to be into in the same way they decide what obscure bands to be into or what fashion trends to follow. See also Applied Nonexistence.
5. Appeal to poverty (argumentum ad Lazarum) – supporting a conclusion because the arguer is poor (or refuting because the arguer is wealthy). Or some other oppressed status.
6. Wishful thinking – a specific type of appeal to emotion where a decision is made according to what might be pleasing to imagine, rather than according to evidence or reason. Extremely popular among anarchists... don't ask why!
7. Tu quoque ("you too", appeal to hypocrisy) – the argument states that a certain position is false or wrong and/or should be disregarded because its proponent fails to act consistently in accordance with that position. A very popular refutation of anti-capitalist and anti-civ positions especially. e.g. http://anarchy101.org/3405/if-you-lot-are-against-hierarchy-why-isnt-everyone-a-mod-lol
I counter logical fallacies by pointing them out.