  In this paper, as a main result, we derive a Chung-Fuchs type condition for
the recurrence of Feller processes associated with pseudo-differential
operators. In the L\'evy process case, this condition reduces to the classical
and well-known Chung-Fuchs condition. Further, we also discuss the recurrence
and transience of Feller processes with respect to the dimension of the state
space and Pruitt indices and the recurrence and transience of Feller-Dynkin
diffusions and stable-like processes. Finally, in the one-dimensional symmetric
case, we study perturbations of Feller processes which do not affect their
recurrence and transience properties, and we derive sufficient conditions for
their recurrence and transience in terms of the corresponding L\'evy measure.
In addition, some comparison conditions for recurrence and transience also in
terms of the L\'evy measures are obtained.
