  The P\'olya number characterizes the recurrence of a random walk. We apply
the generalization of this concept to quantum walks [M. \v{S}tefa\v{n}\'ak, I.
Jex and T. Kiss, Phys. Rev. Lett. \textbf{100}, 020501 (2008)] which is based
on a specific measurement scheme. The P\'olya number of a quantum walk depends
in general on the choice of the coin and the initial coin state, in contrast to
classical random walks where the lattice dimension uniquely determines it. We
analyze several examples to depict the variety of possible recurrence
properties. First, we show that for the class of quantum walks driven by
independent coins for all spatial dimensions, the P\'olya number is independent
of the initial conditions and the actual coin operators, thus resembling the
property of the classical walks. We provide an analytical estimation of the
P\'olya number for this class of quantum walks. Second, we examine the 2-D
Grover walk, which exhibits localisation and thus is recurrent, except for a
particular initial state for which the walk is transient. We generalize the
Grover walk to show that one can construct in arbitrary dimensions a quantum
walk which is recurrent. This is in great contrast with the classical walks
which are recurrent only for the dimensions $d=1,2$. Finally, we analyze the
recurrence of the 2-D Fourier walk. This quantum walk is recurrent except for a
two-dimensional subspace of the initial states. We provide an analytical
formula of the P\'olya number in its dependence on the initial state.
