An anecdote (not to be confused with the thing one takes after one is poisoned) is a short and amusing or interesting story about a real incident or person, often used fallaciously as evidence in an argument. A good anecdote is memorable, good at making people feel emotional, effective at changing opinions, and rarely has any valid connection to the argument.
Here are three things to keep in mind when hearing or reading an anecdote:
1) They are often bogus. You know that kid "Mikey" on the Life cereal commercials? He drank soda with Pop Rocks and his stomach exploded.
2) They are all too common. There is an anecdote for virtually any position. Should you ever lie? There was this little boy whose nose grew each time he lied. There was this woman who divorced her husband for his answering "yes" to the "does this dress make me look fat" question.
3) They are untrustworthy. Anecdotes that are based on truth are commonly greatly exaggerated through the telling and retelling process. In high school, I got a black eye when I clumsily opened up the car door with my eye in the way. By the end of the week, the story morphed into me being attacked by three guys, two of whom I sent to the hospital (BTW, I never bothered correcting that story).
An anecdote as evidence is about the same value as a poorly conducted and highly flawed study with a sample size of one. They work so well because we generally prefer stories and emotion to facts and logic. They are powerful rhetorical devices and should be used to entertain and even drive home a point, but rarely as evidence. Because this one time, this babysitter... forget it.