The bottom line of the "Analytic Continuation" page on WolframMathWorld states:
there exists a meromorphic function in the unit disk where every point on the unit circle is a limit point of the set of poles.
I must admit that I've been rather surprised by such a statement, therefore I tried to construct this example by myself and to google for it, but nothing came up. Do you have any idea on how such a function looks like?
Thanks in advance!