Bandwidth and power constraints are the main concerns in current wireless networks because ad hoc mobile wireless networks rely on each node in the network to act as a router and packet forwarder. This dependency places bandwidth, power, and computation demands on mobile hosts which must be taken into account when choosing the best routing strategy. In recent years, protocols that build routes based ``on demand'' have been proposed. The major goal of on-demand routing protocols is to minimize control traffic overhead. In this paper, we perform a simulation and performance study on some routing protocols for ad hoc networks. Distributed Bellman-Ford, a traditional table-driven routing algorithm, is simulated to evaluate its performance in multihop wireless networks. In addition, two on-demand routing protocols (Dynamic Source Routing and Associativity-Based Routing) with distinctive route selection algorithms are simulated in a common environment to quantitatively measure and contrast their performance.