"Do you still beat your wife?"
Either way you answer, you're an asshole.
Or "He worships his Jeri Ryan poster every day, doesn't he?"
"No, he doesn't" is insufficient; they could then crash on you worshipping the poster every other day or the like (note the italics above).
If you say, "Yes, he does," well...you get the idea.
The golden mean is interesting. Many do this without even thinking about it. In the versus community it typically takes the form of something like this:
"The White Star's lower-limit firepower is 5W, and its upper-limit is 12,500 TW. Therefore, to know its true firepower, look somewhere in between."
While somewhere "in between" IS probably closer to the truth, that is not a valid way to arrive at a figure (see bottom for some difference between truth and validity).
Be sure that, anytime you encounter a person who wants to use such a method in a semi-formal debate, you either do not allow it or you are quick to whip it out when the debate gets to the stage of questioning each others' ability to reason. You have a big, fat example to throw in his/her face.
Hmm...let's see...what to say...
Abusive ad hominems are pretty common, but some mistakenly believe it's any insult, which is wrong. It's only fallacious if it's an insult without a logical argument. E.g.,
"It is raining outside.
Rain is wet.
Therefore, it is wet outside, ASSHOLE!" is not an ad hominem attack.
A true ad hominem:
"Michael Jackson said he did not have more than two facial surgeries.
But Jackson is one weird motherfucker.
Therefore, he must be lying...I bet he had three or more surgeries."
Less common is the Tu Quoque variant of the ad hominem. It literally means "you too":
"You drink five gallons of whiskey a day, dad, so it's okay for me to do that too."
I considered using a form similar to this about a half hour ago. In an argument with some Cowboy Bebop fans, it was suggested that I should watch more of the show before forming an opinion (w/ which I partly agree, but not totally).
I was about to retort, knowing that the following (stated as such) was fallacious: "Well, you guys probably bash 'Enterprise' and you don't intend to watch one more episode, ever, let alone all of them; therefore, I can do the same thing with Cowboy!"
Well, I could, but it would be illogical. Bad bad. Zathras no like bad.
Instead, I simply used the ENT thing as an analogy, to illustrate that forming a dislike for a character (for instance) doesn't require me to watch all aired episodes of CB; such is as sure a false dilemma as it would be to tell someone they must watch all ENT episodes before they can form a dislike for Hoshi worth airing in an online community. (I didn't put quite that fine a point on it at the time because I was a bit mad and tired at that very moment, however. One should not post when angry or tired!

Other popular fallacies...hmm...I would qualify "appeal to authority" as an illicit appeal to authority (or illicit authority), for you can make a perfectly valid argument based on someone else's "authority" as such. Almost all valid arguments depend on this to a certain extent, even if it's at a Cartesian level.
For instance, an appeal to illicit authority would read:
George Bush says pollution causes cancer.
Cancer is bad for us.
Therefore, pollution is bad for us too.
That'd be ok if you weren't asking an unqualified "expert" like George Bush what he thought about cancer; but he's the U.S. President, which does not require expertise on diseases or pollution!
But if you said C. Everett Koop says something causes cancer, he ought to know. You'd have to get that information from somewhere, though you raise red flags when you take pains to mention the source in the simpler syllogistic forms. If you are arguing with someone that is vaguely familiar of the fallacies, leave off the actual "appeal" itself, no matter the source. Some neophyte idiot will probably try to divert the issue by incorrectly dismissing your argument as "authority appeal." And to crank out a slippery slope of my own, chances are good that they'll go on to start attacking that source's person; e.g, "Mike Wong can be mean, wanh!, so he doesn't know what he's saying!" or "Mike Wong is biased so he is wrong!" One fallacy begets another sometimes

And how about false cause?
"I was about to hit myself on the head with a hammer.
I suddenly dropped dead.
Therefore, even preparing to hit yourself will kill you."
The most relevant popular example false cause in vs. debates is the whole bit of fighters shooting a dome on Executor, which people then take to mean, "Oh, those are SHIELD DOMES! The fighters shot them, and that caused the shields to drop!"
Appeal to the stick? This sort of chest-beating is somewhat rare, and often confused with posturing, but it's when the threat itself takes the form of an argument that you run into trouble, like:
"I can kick your ass. What you say, therefore, is wrong."
Also, as others have pointed out, false dilemmas (often taking the form of the false dichotomy) and straw men are completely different things.
A false dichotomy, for instance, is a fake either/or scenario thrust upon you, wherein you must choose between two things; a straw man is when you distort someone else's argument, attack the distortion, then claim to have whipped their original positon. It is often confused with the red herring, but simply think of it this way: red herrings change the subject, while straw men twist your words or put words in your mouth.
If, for example, you said something like, "That guy is not smart," a straw man would begin by claiming you said, "That guy is retarded," and a red herring would discuss some irrelevance about, oh, say, intelligence or unsmart people's breeding habits, perhaps.
Bandwagon appeal, similar to the appeal to authority (only this time, you're talking about more than one person; you're talking about a huge group of people), is rarely seen in a respectable discussion forum, but it's still prone to pop up from time to time:
"90% of people think dietary fat makes you fat.
Therefore, dietary fat does make you fat."
Or more pertinent to these parts, something we've all heard before:
"Most Star Trek fans think ST technology is more advanced than stuff we see in Star Wars.
Therefore, it must be true."
One anyone could relate to:
"Much of Europe at one time thought the world was flat.
Therefore, at that time, the world was flat."
In general, if you want to argue successfully...do NOT run with what's simply "popular belief"! The masses can be startlingly simple-minded.
Let's see...Ooo! The context-dropping fallacy, sort of a few other fallacies crammed into one:
"In Star Wars, fighters are useless against capships.
Star Trek has capships also.
Therefore, fighters would be useless against Star Trek capships too."
I love talking about fallacies; I fell in love with logic in the early spring of 1997, even some of the worthless symbolic shit

But first--Tom, you said:
It's actually a number of fallacies rolled into one, depending on how you look at it, but you have to try to look at the argument in its entirety...don't get bogged down looking at the false dichotomy of "either you understand Plato and are smart, or you don't understand because you're dumb" just yet, as that is only a single premise. You want to speak to the validity or invalidity of the entire argument w/ which you're faced...See, my impression -- using example 1 -- is the following statement:
Everyone who understands Plato likes Plato. You do not like Plato; therefore, you do not understand Plato.
Which would, then, be an example of "A, therefore B." I think. I try never to be too sure of myself in these things.
So if I was to give one fallacy top-billing here, I'd give it to begging the question, because the premise--if you understand Plato, you like Plato--is the same as the conclusion; it's simply worded differently.
You might say that if we isolated the argument's premises to look for fallacies, we'd be going about a hasty generalization in that we didn't look at the whole argument

Put another way, do not treat invalid and "untrue" as synonymous. I oftentimes slip up and do this because the distinction isn't firmly reinforced in our everyday language...for that matter, most things are not beyond linguistic routines ("Hey, how are you?" "Fine," etc.).Stating facts, even if those facts are false, is not fallacious. It may be incorrect, it may even be dishonest, but a logical fallacy invariably requires a proposition of the general form "A therefore B" in which A does not actually lead to B.
When we say, "Ah, that's just not valid," we register: "INVALID, BULLSHIT, FALSE, UNTRUE." But invalid arguments can certainly have very truthful premises, like the one above about pollution being bad for us; how you use that to draw a conclusion, however--that process you follow to come to some determination--is where the fallacies might come into play.
Someday, just for fun, I intend to compile the best fallacies I can find into one big document. Lord Wong has already done this successfully here, but I think I might do it with a Babylon 5 twist to submit to Babtech. Especially a couple of years ago, listening to some Babylon 5 fans' arguments was at least as thorough a study in fallacious reasoning as listening to the most infamous vs. community Trekkies.
But I swear, the very best place to hear fallacies is from my barber. He is a dear man, if I can say that without sounding gay, and I've known him for 18 years or so--great guy. I'd give him the shirt off my back.
But damn, he is flat-out dumb sometimes. I can think of no other, more delicate way to euphemize that. He is a born-again Christian who believes in all kinds of conspiracy theories that his preacher (or someone at his church) tells him, like shit about "the New World Order" led by Satan, George Bush Sr., and a bunch of other junk.
Anyway, if the subject of war comes up, he is quick to talk about Muslims, specifically how "...their God didn't rise from the dead!"
I take it he means something like this:
"A religion in which your God takes a flesh form, dies, then is resurrected is superior to a religion with a god that doesn't take flesh, etc.
Christianity has such a God. Islam does not. Therefore, Christianity is superior to Islam."
Well, DUH, Wayne: Mohammed never claimed to be Allah, so why is it unremarkable that Mohammed--a prophet of pure heart, says the Qu'ran--doesn't rise up from the grave? Massive context-dropping, among other things...it actually becomes such a bad comparison that it makes my eyes cross!
And I must confess, I get frustrated by the man's hasty generalizations. For instance, I am a bodybuilder. I train very heavy, balls to the wall, but my workouts are brief (valid dichotomy here: you can either work as hard as possible whilst still maintaining a certain level of productivity, or can work for long periods, but not both). When people ask me, "How many sets do you do of presses and curls?" they are dumbfounded when I say, "One hard set of all the exercises I do."
So my barber asks me how my training is going. I tell him, great, I'm training twice a week at the moment (as I was at that point; I'm training 3x/wk. at the moment but with lower volume of work/workout, for those interested

Suddenly, he blurts, "Just enough to maintain, huh?!" I crinkled my nose. "What? Maintain? No. I want to be bigger than a house," I said. "Why would I train to just be maintaining?"
He, of course, was operating under the assumption that to get really big, you must train every day of the week for hours on end; and that, consequently, anyone who did far less than this wasn't out to get bigger. It took ages to explain to him that less work is in most cases MORE desirable; that you shouldn't apply the same kinds of rules you would to further aerobic training to anaerobic training.
I bet barbershops everywhere are just teeming with fallacious bacteria.