  We discuss the relation between bulk topological invariants and the spectrum
of surface states in three dimensional non-interacting topological insulators.
By studying particular models, and considering general boundary conditions for
the electron wavefunction on the crystal surface, we demonstrate that using
experimental techniques that probe surface states, only strong topological and
trivial insulating phases can be distinguished; the latter state being
equivalent to a weak topological insulator. In a strong topological insulator,
only the {\it parity} of the number of surface states, but not the number
itself, is robust against time-reversal invariant boundary perturbations. Our
results suggest a $\z$ definition of the bulk-boundary correspondence,
compatible with the $\z$ classification of topological insulators.
