When I was a kid, long before the word "meme" was in popular usage, there was a meme that said "science says bumblebees can't fly". It was usually repeated by people who wanted to prove that scientists were stupid. Many but not all of the people repeating this story were trying to cast doubt on something else scientists say, quite often the theory of evolution. In general, scientists are both not stupid and unlikely to make statements proven false by actual experience. Where did this story start?
According to Cecil Adams* at The Straight Dope website, this story came about because of a discussion between some German scientists at a dinner party. A physicist did some quick calculations and determined the bumblebee could not flap her relatively small wings fast enough to produce the necessary lift. A biologist heard this, and wanting to show up someone from "the hard sciences", spread the story far and wide. As Adams puts it, once the physicist sobered up, he saw his error. The number of firings by the bee's nervous system does not produce enough flaps, but the wings vibrate many times per flap, not unlike a string vibrates many times on one pluck or a drum head vibrates many times when hit only once. The vibrations account for the extra necessary wing movement, and science tells us what we already knew, bumblebees fly. The difference is, now we know how and the answer is not one that could be arrived at using that over-rated commodity, "common sense".
I bring this up because there are still people wishing to discredit some part of science, and they often try to do so by bringing up some story to show that science has been wrong before. Without question, scientific knowledge changes, sometimes refining an idea, sometimes overthrowing it completely when a new revolutionary theory explains all the data previously explained and reconciles puzzling evidence the old theory could not. Mathematics, my field, isn't quite as fickle, but it also isn't quite as useful.
While there are still people trying to cast doubt on evolution, the theory that is being hit hardest right now is anthropogenic climate change, the idea that human action has something to do with with general warming trend of the past hundred years or so. It is the standard model used by climate scientists, and it is possible that it could be overturned, but if it is, it will be overturned by a truly better theory that explains all the data at least as well and in some cases better. It will not be overturned by the wishful thinking of people who just don't want to stop making obscene profits or just don't want to alter their overly comfortable life style.
*(Note: Adams answered this question in 1990 and the source link he gives is dead. If anyone can find an earlier source, I'd be glad to make a link to it.)