The thing I always think of when someone tries to present anecdotes as evidence is just how fallible our perception and memory are. Many magicians and mentalists tell you up front they have no supernatural powers, yet they still are able to trick our minds into seeing amazing things. Our memories also change over time. Steven Novell, a neurologist form Yale university says "In fact it [the memory] is likely to change in a way specifically to give the story more meaning, while sacrificing factual accuracy."
The bottom line with anecdotes is they are really bad evidence. If you have lots of anecdotes you still don't have any good evidence; you have a pile of bad evidence. It is worth noting that anecdotes can be a good place to start research. When you get into trouble is when they are the end of your research.
For more information check out the Skeptics Dictionary