There are some cases that people get the shot and still get the flu, but often it's because they didn't get it early enough. I don't get flu shots but really it's just because I never did and am stuck in my ways, not because of any fear of them. As noted below, the "causes Autism" thing is a lie perpetrated by people that have no clue what they're talking about.
Flu shots are basically for the very young, the very old, and/or the very weak. For the vast majority of people, flu shots do not result in any adverse reactions. The autism scare died down after being paraded around by scientifically illiterate celebrities. Flu shots work for the same reason people recover once they are sick.
Yes, flu shots work. That is they work at least as well as the manufacturers can guess which strains of flu virus will be present in any given year. A combination of up to 13 strains of the virus are combined into each year's flu shots. Usually, the manufacturers get the correct one among the group chosen and the threat of the flu is lessened considerably. Those with depressed immune systems need to get flu shots because without them the flu can be fatal.
While they are not always a perfect match to the current strain, in general flu shots do work. They frequently prevent those who get them from catching the flu, and those who still catch it get a much milder case that they get over more quickly. A flu shot is an essential level of protection.