The timely processing and dissemination of information over wireless sensor networks is a key aspect of their future success. This is especially important for delay-sensitive applications such as detection and estimation. This paper assumes a two-tier architecture for wireless sensor networks where sensor nodes are simple devices equipped with one antenna, and cluster heads are more powerful units endowed with multiple antennas each. The cluster heads collect information from the sensor nodes, process data locally, and then relay pertinent information across the network. This article studies the potential benefits of having multiple antennas at the cluster heads on the data collection and dissemination operations. The focus is on delay-sensitive traffic, and performance is measured in terms of effective capacity. Analysis shows that, for Gaussian channels, having multiple antennas at the receiver results in a power gain, while having multiple antennas at the transmitter provides a statistical gain. In both scenarios, the data rate that a wireless channel can support is increased significantly through the use of multiple antennas at the cluster head. Numerical results confirm that the gains of a multiple-antenna configuration over a single-antenna link are substantial for delay-sensitive applications. This provides support for the two-tier architecture studied in this paper and for cluster heads having multiple antennas.