Anecdotal evidence
http://en.wikipedia.org/wiki/Anecdotal_evidence

Anecdotal evidence is evidence stemming from a single, often unreliable
source which is used in an argument as if it had been scientifically or
statistically proven. The person using anecdotal evidence may or may
not be aware of the fact that, by doing so, they are generalizing.

For example, someone who is not a physician or other kind of expert
might argue that eating crushed garlic and drinking one glass of red
wine per day will prolong your life, just because their own neighbour
indulged in that habit and died aged 90. It becomes clear that in this
case any form of inductive reasoning lacks a broad empirical basis.

Similarly, a politician might publicly demand better teacher training
facilities just because their own son or daughter happens to have a
spectacularly incompetent teacher.

This is not to say that anecdotal evidence is fallacious per se; it
just depends on how it is used. In many cases, it can be the starting
point rather than the result of scientific investigation.

See also

logical fallacy

faulty generalization (overview)

hasty generalization

anecdote
http://en.wikipedia.org/wiki/Anecdotal_evidence