The Bonferroni correction is used to account for increased experimentwise error rates when testing multiple hypotheses. Experimentwise error rates are used to describe the increased chances of committing a Type I error when running multiple chi-squares, t-tests, ANOVAs, and other statistics concurrently. You are simply more likely to detect statistical significance by chance with the more statistical tests that you run.
The Bonferroni correction keeps researchers HONEST in regards to reporting significant main effects of clinical merit. It further deters researchers from making erroneous conclusions based on large sample sizes and implausible effect sizes.
In order to calculate the Bonferroni-corrected alpha value to achieve statistical significance when testing multiple hypotheses concurrently, divide the alpha value of .05 by the number of hypotheses you are testing. So, if I was assessing the differences between men and women on four (4) different outcomes, (.05 / 4) = .013. This means that the inferential statistic for any of our four outcomes would have to be less than .013 to be statistically significant (rather than just being lower that the normal .05).
Publications have caught on to the utility and relevance of the Bonferroni correction. Some journals specify its use in the author guidelines and will reject manuscripts automatically if the correction is not used for multiple hypotheses.
In conclusion, use the Bonferroni!