We consider a communication type queueing network in which data packets are injected over time and form queues at the nodes of the communication links. A packet scheduling policy is defined to be stable if it leads to bounded queue lengths. To the day no algorithmic characterization exists for checking stability of a given scheduling policy in a given queueing network. We first provide a very simple classification of network topologies which are stable under any work conserving scheduling policy. Then we construct a certain class of scheduling rules, for which the stability is algorithmically undecidable. On related note, we show that stability of a homogeneous random walk in a non-negative orthant is undecidable. The stability of other scheduling policies like First-In-First-Out and priority policy is also conjectured to be an undecidable problem.