Any example of a connected space that is not locally connected? A topological space $X$ is said to be locally connected at a point $x \in X$ if, for every neighborhood $U$ of $x$ (i.e. open set $U$ such that $x \in U$), there exists a connected neighborhood $V$ of $x$ such that $V \subset U$. If $X$ is locally connected at each of its points, then it is said to be locally connected. 
Now is there any easy enough example of a connected space that fails to be locally connected at some point? 
One example adduced by Munkres is the so-called topologist's sine curve, but I'm not sure why it is not locally connected. 
Any other examples, please? 

Another standard example that is even path connected but not locally connected is the comb space
$$ [0,1]\times\{0\} ~\cup~ \{0\}\times[0,1] ~\cup~ \bigcup_{k\ge 1} \{\tfrac1k\}\times[0,1] $$
Every neighborhood of the point $(0,1)$ contains the top end of infinitely many of the teeth, but if the neighborhood is so small that it doesn't contain the base of the comb, it will be disconnected -- and making it smaller cannot possibly make it connected.
