In recent years, the use of wireless sensor networks for industrial applications has rapidly increased. However, energy consumption still remains one of the main limitations of this technology. As communication typically accounts for the major power consumption, the activity of the transceiver should be minimized, in order to prolong the network lifetime. To this end, this paper proposes an Adaptive Staggered sLEEp Protocol (ASLEEP) for efficient power management in wireless sensor networks targeted to periodic data acquisition. This protocol dynamically adjusts the sleep schedules of nodes to match the network demands, even in time-varying operating conditions. In addition, it does not require any a-priori knowledge of the network topology or traffic pattern. ASLEEP has been extensively studied with simulation. The results obtained show that, under stationary conditions, the protocol effectively reduces the energy consumption of sensor nodes (by dynamically adjusting their duty-cycle to current needs) thus increasing significantly the network lifetime. With respect to similar non-adaptive solutions, it also reduces the average message latency and may increase the delivery ratio. Under time-varying conditions the protocol is able to adapt the duty-cycle of single nodes to the new operating conditions while keeping a consistent sleep schedule among sensor nodes. The results presented here are also confirmed by an experimental evaluation in a real testbed.