One of the most prevalent myths of homebrewing is Hot Side Aeration. HSA is the effect of O2 oxidizing your wort at hot temperatures, and is caused by agitating the hot wort. The more agitation and splashing, the more HSA will supposedly occur. HSA off flavors include musty, cardboard, or paper aromas/flavors. It is traditionally thought that the time period between the end of the boil and when chilled is when HSA can occur (I am not sure at which temperature the classic literature says that HSA is no longer an issue, but one old Zymurgy article says 86 degrees F!). There have also been claims that too much agitation of the mash can cause HSA, although most information these days says that the boil will reverse any HSA in the mash. From what I understand, beer oxidizes naturally, but at higher temperatures it oxidizes much easier due to the increase in energy (heat = energy). That is why we store our beer long term in the fridge.
Introducing Dr. Charlie Bamforth, one of the leading brew scientists at UC Davis. He has done a lot of research on behalf of Anheuser-Busch, including research on HSA. He says that HSA, while not a complete myth, is something that professional brewers and especially homebrewers shouldn't worry about. First of all the small scale at which homebrewers brew produces such a smaller amount of splashing in comparison to prouction breweries. In addition with a healthy fermentation the yeast will clean up any effects of HSA.
For more details, check out this interview with Dr. Bamforth. It is one of the best episodes of the Brew Strong podcast: