I've found that a lot of lists of fallacies accidentally bring entirely new fallacies into being, from people misunderstanding and overgeneralizing the old fallacies.
Strawman - or, Referring to the Opponent's Position
Person 1: We should ban cryopreservation, because it gives the rich an advantage over the poor. Person 2: My opponent believes that we should ban cryopreservation- Person 1: Strawman fallacy!
False Cause Fallacy - or, Appeal To Bayes
Person 2: It is a consistently demonstrated fact that smokers are vastly more likely to have lung cancer, and people with lung cancer are vastly more likely to be smokers- Person 1: False cause fallacy! Person 2: One could theorize that there are confounding factors, but I invite you to look for them. There are none- Person 1: False cause fallacy!
Appeal To Emotion - or, Assumption That Moral Values Are Present
Person 2: My opponent's policy of preventing overpopulation by shooting random passersby has led to demonstrable harm, as seen here, here, here- (bang) Person 1: Appeal to emotion! Come up with an actual argument, next time, why don'tcha?
Moving The Goalposts - or, Not Being A Strawman
Person 1: My opponent believes we should kill and eat babies! Person 3: No, I don't? We were arguing about tax rates. Person 1: Special pleading! Moving the goalposts! Not being a strawman!
Personal Incredulity - or, Appeal To You're Making No Fucking Sense
Person 1: We should send rationalists to the moon so they can experience explosive decompression! This will please the Great Mortimer Mouse who lives there, and hates rationalists! We will experience healthy rains for our crops! Person 3: What- Person 1: Personal incredulity!
Tu Quoque - or, Ignoring Dibs
Person 1: My opponent believes that we should ban cryopreservation! Person 3: Actually- Person 1: Tu quoque!
The Gambler's Fallacy - or, Appeal To Probability En Masse
Person 3: Listen, I know you like driving your car off this broken bridge, but we can't count on landing safely every time- Person 1: Every event is statistically separate! Gambler's Fallacy! Woo! (crash)
Bandwagoning - or, Membership In A Large Group
Person 4: Actually, believe it or not, your perpetual motion machine will not work, and here's why- Person 1: Wait! Other people said that, too! Bandwagoning!
Appeal To Authority - or, Appeal To Expertise
Person 4: No, really, I'm a physicist, I've studied what you're talking about for a living, it doesn't work. Person 1: Appeal to authority!
Appeal To Nature - or, Appeal To Reality
Person 1: Now I'm going to train pigs how to fly by feeding them chicken feathers I mashed up with my teeth, thereby giving them bird DNA for wings and the human intelligence to use them! Person 4: No, that's not even how DNA works- Person 1: Appeal to nature!
Ambiguity - or, Failure To Be Idiot-Proof
Person 4: Hey! Stop dangling me off of the side of a building! Put me down, you - no! (splat) Person 1: Ambiguity!
Begging The Question - or, Attempted Use Of A Schelling Point
Person 5: While your policy ideas are quite humorous, I think we should look for a way to accomplish the same ends without killing half of the population. Person 1: What? Why? Begging the question!
False Dilemma - or, Argument By Elimination Of Possibilities
Person 5: Look, the money for your proposal needs to come from somewhere. Unless our revenue is increasing - and you don't seem to think it is - we need to cut some other program; which one do you think we can cut for this? Person 1: None of them! That's a loaded question! I didn't say to cut anything! False dilemma!
Anecdotal Fallacy - or, Appeal To Evidence My Theory Doesn't Explain
Person 5: My friend, Tom, is black, and he seems to have all the mental faculties I expect of a human being. Perhaps you should reconsider your idea that nonwhite races are subhuman and unfit to participate in society. Person 1: Anecdotal fallacy!
The Texas Sharpshooter - or, The Scientific Method
Person 5: Well, we tested five theories, and the evidence disproves Theories A and D, strongly suggests Theory B- Person 1: Texas Sharpshooter! (bang)
Middle Ground Fallacy - or, Not Being Insane
Person 6: No, I don't want to kill all old people, but that doesn't mean I do want to kill all babies! Person 1: Ugh, fucking pussy! Pick a side! It's old people or babies! What a load of liberal "truth is in the middle" bullshit! You probably watch a lot of South Park! Person 6: Actual false dilemma! Person 1: Middle ground fallacy!
Genetic Fallacy - or, Wariness Of Archnemeses
Person 6: Baron Evil Von Kickspuppies, I somehow don't trust your plan to give food to the poor, particularly seeing as you've refused to permit tests for poison. You've also sincerely argued for killing all babies, not five minutes ago. Person 1: Genetic fallacy!
Ad Hominem - or, Appeal To Accountability
Person 6: My opponent has killed the entire homeless population of the United States, and has yet to be brought to justice! Clearly, he does not deserve your vote for president! Person 1: What a disgusting attack on my character - and a refusal to address my actual arguments, too! Ad Hominem!
No True Scotsman - or, "No, You're Not A Goddamn Scotsman"
Person 1: Well, as a Jew, I personally believe we should all be sent to concentration camps. Person 6: Wait, you're a Jew? What are your religious beliefs? Person 1: I'm an atheist. Person 6: So it's your parents or grandparents or something? Person 1: Nope, my family tree is pure Aryan! Person 6: How are you a Jew, then? Person 1: No True Scotsman!
Fallacy Of Composition And/Or Division - or, Failure To Consider That A Miracle Occurred
Person 6: That's not a computer, it's a two by four with a nail sticking out of it. (wham, wham, wham) Person 1: Fallacy of composition and slash or division.
Burden Of Proof - or, Appeal To Lack Of Coherent Counterarguments
Person 7: Evolution is, in fact, how life on Earth developed. Person 1: The burden of proof lies with you. Person 7: True. Here's a vast body of evidence in support of my position. Person 1: The burden of proof lies with you. Person 7: But I have demonstrated it, haven't I? Person 1: The burden of proof lies with you. Person 7: You're kind of begging the question, aren't you? Person 1: The burden of proof lies with you.
Slippery Slope Fallacy - or, Appeal To Future Consequences
Person 7: Listen! People! Applying the sterilization process to everyone at birth doesn't sound so bad, given that it's reversible - but if future congresses change their mind about the whole personal liberty thing, they could easily outlaw the antidote! In fact, my opponent, Senator Von Kickspuppies, has said that's exactly what he wants! Person 1: Slippery slope fallacy!
The Fallacy Fallacy - or, No, Stay Here, I'm Not Through, Keep Listening To Me, P-P-Please
Person 7: Senator, I have followed all of your public positions for years. Not a single one of them has made any sense whatsoever; there has been no logical coherency whatsoever. This new bill you've drafted looks no different. Person 1: Fallacy fallacy!