Slippery Slope – this is a false extrapolation. It is the claim that one event will lead to its extreme.
Common example: "They’re making us register our pistols and rifles. Next thing you know, they’ll take away our guns altogether." This is like saying we need driver’s licences—soon they’ll take away our cars.
Evolution/creationism: "They’re trying to teach children evolution. Next thing you know, they’ll ban religion altogether." There is no evidence for this whatsoever.

Special Pleading – This is a last ditch appeal to accept a weak or collapsed argument for unrelated reasons.
Common example: "So what if certain people believe in a disproven alternative cure. They’re not hurting anyone." If someone has a seemingly benign belief, it isn’t necessarily harmless. A belief in a harmless cure may prevent someone from getting a proven cure. They might die not from what they took, but from what they didn’t.
Evolution/creationism: "If people wish to believe in creationism, then where is the harm in that?" If the majority elects politicians who form policy to remove the teaching of one of the foundations of biology thus eroding science education, then this will lead to greater scientific illiteracy in your population over time. A well-informed society is better able to make well-informed decisions.

Strawman – to create a silly caricature of your opponent or opponent’s position in order to give them less credibility.
Common example: "These nerdy, geeky scientists with their pocket protectors and greasy hair say that an asteroid might hit the Earth at some time in the future. Hah! I think they've been reading too much science fiction or smoking something!"
Evolution/creationism: "So these paleontologists say that we descended from… monkeys? Excuse me?" Since monkeys are generally considered "goofy" and the apparent absurdity of little monkeys being our grandparents, the arguer is attempting to destroy the credibility of the idea of human decent from other primates by making the whole idea sound preposterous.

Some chimpanzees considering having descended from... monkeys?