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.
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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.

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?