A wireless sensor network (WSN) is a collection of sensor nodes distributed over an area of interest to accomplish a certain task by monitoring environmental and physical conditions and sending the collected data to a special node called sink. Most studies on WSNs consider nodes to be powered with irreplaceable batteries, which limits network lifetime. There are, however, perpetual power source alternatives as well, including mains electricity and energy harvesting mechanisms, which can be utilized by at least some portion of the sensor nodes to further prolong the network lifetime. Our aim here is to increase the lifetime of such WSNs with heterogeneous power sources by centralized or distributed routing algorithms that distinguish battery- and mains-powered nodes in routing, so that energy consuming tasks are carried out mostly by mains-powered nodes. We first propose a framework for a class of routing algorithms, which forms and uses a backbone topology consisting of all mains-powered nodes, including the sinks, and possibly some battery-powered nodes, to route data packets. We propose and evaluate a set of centralized algorithms based on this framework, and our simulation results show that our algorithms can increase network lifetime by up to more than a factor of two. We also propose a fully distributed power-source-aware backbone-based routing algorithm (PSABR) that favors mains-powered nodes as relay nodes. We validate and evaluate our distributed algorithm with extensive ns-2 simulations and our results show that the proposed distributed algorithm can enhance network lifetime significantly with a low control messaging overhead. Besides wireless technology independent routing solutions, we also propose a technology specific power-source-aware routing solution (PSAR) for sensor and ad hoc networks which use 802.15.4/ZigBee as the wireless technology. Our solution is fully distributed, tree-based, and traffic-adaptive. It utilizes some protocol specific properties of ZigBee, such as distributed and hierarchical address assignment, to eliminate battery-powered nodes on the routing paths as much as possible. To validate and evaluate our ZigBee-specific algorithm, we first implemented ZigBee extensions to ns-2 simulator and then implemented and simulated our protocol in this extended ns-2 environment. Our results show that the proposed algorithm operates efficiently and can increase network lifetime without increasing the path lengths significantly, compared to the default ZigBee routing algorithm.