Wireless sensor-actor networks (WSANs) are applicable in versatile domains ranging from very common to those which demand reliable actions in the event area. The unique characteristics of WSANs and the resourceconstrained nature of the constituent sensor nodes give rise to design energy and delay efficient routing protocols. Many researchers have made considerable efforts to meet these challenges by designing energy and delay efficient protocols. In this paper, a comprehensive survey is presented on existing routing protocols for WSAN to analyze and list out their merits and demerits. The study broadly segregates the existing routing protocols into two categories i.e., cluster based and non-cluster based protocols. The cluster based protocols structure the physical network into virtual groups, whereas the non-cluster based protocols either use flooding or broadcasting mechanisms for communication. All the routing protocols under consideration have been simulated in a common simulation platform. Their performances are analyzed with respect to average end-to-end delay, packet delivery ratio, and average energy dissipation in the network individually. In addition, the best protocols among both the categories are compared to derive an overall conclusion.