Strawman Fallacy

See Idea Channel's explanation of the fallacy here.

The Strawman Fallacy occurs when a debater constructs a more easily defeated version of his opponent's position to attack, rather than addressing his real arguments. The fallacy takes its name from straw dummies used in old-fashioned combat training; these dummies were made to look like a potential opponent, but provide no actual resistance. The fallacy itself is comparable to defeating such a dummy, then proclaiming you have defeated an actual opponent.

"The NRA supports the right to bear arms, so they support private ownership of nuclear weapons."

While most people will not be fooled by a blatant misrepresentation of their position, careful use of a strawman can make them defend a carefully undermined version of their position, allowing their opponent to apparently destroy them with a prepared rebuttal.

Examples of Strawman Fallacy include:

See The War On Straw.
Beloved of Author Tracts the world over.

Looks like this fallacy but is not

When the argument being refuted is not misrepresented.

Red Herring

While a Strawman will extrapolate details into a second, weaker argument in order to apparently defeat the first, a Red Herring will establish a second, different argument to try to make everybody else involved forget about the first one.

Alice: Health Insurance is too expensive. Something must be done to bring down the costs.
Bob: It wouldn't be so expensive if doctors didn't order so many unnecessary, expensive tests.
Alice: Most of those tests are not unnecessary! They save lives!

Bob has successfully sidetracked Alice from the cost of health insurance to the necessity of many medical tests.

Rigged Match Making

Close to Red Herring, but instead of diverting the subject somewhere else entirely, a debater narrows the scope of contest down to an area where the argument can be reliably won. Replace the challenged with the strongest from your camp - or challenge the weakest in the opponent's (perceived) camp. Explained with some references here and here.

Motte and Bailey Doctrine

Retreat from the fight to the safety of an obvious, uncontested statement. Sit out the attack, then return to business as usual.

Weak Man Fallacy.

Attack the weakest position you can find in the opponent's camp, then claim you defeated the whole army.

It's not "Hitler Ate Sugar", because this time the attacked subject is at least somewhat relevant. Oh, it's still jousting against a straw man on a dead horse - but at least the horse once was actually alive and even moved in your general direction.

Oddly enough despite the metaphor, in actual military tactics it is often the case that if you defeat the weakest position you defeat the army-because you spread panic, expose supply lines, permit attacks on other units, etc.

No, YOU Come To ME

Both together. Since one of these tricks is a cheating attack strategy, and another is a cheating defence strategy, of course, this can and often does end up with both opponents claiming the rights for that big juicy middle ground, yet unwilling to oppose each other any closer than by shouting "If you're not a coward, why won't you come here and fight me?" over it.

Suppose we’re debating feminism, and I defend it by saying it really is important that women are people, and you attack it by saying that it’s not true that all men are terrible. Then I can accuse you of making life easy for yourself by attacking the weakest statement anyone vaguely associated with feminism has ever pushed. And you can accuse me if making life too easy for myself by defending the most uncontroversially obvious statement I can get away with.
So what is the real feminism we should be debating? Why would you even ask that question? What is this, some kind of dumb high school debate club?

Accent

Also Called

Amphiboly

A sneakier form of Strawman; here, rather than actually altering their opponent's words, a debater shifts emphasis to make their opponent appear to be saying something else. For example, "We should not speak ill of our friends" (stating we should be kind to friends) becomes "we should not speak ill of our friends" (we can speak ill of anyone else). Commonly used for humour value if it involves a Suspiciously Specific Denial, but it's still a fallacy if used as part of an argument; like Strawman, it's an attempt to evade addressing the opponent's real point.

Bob: I can't believe some people. I'd never do anything like that with a domesticated horse, it's despicable.
Alice: Prefer them wild, do you?