Anytime, anywhere network connectivity, together with portable sensing and computing devices have led to applications in which sources, for example people or environmental sensors, send updates of their status, for example location, to interested recipients, say a location service. These applications desire status updates at the recipients to be as timely as possible; however, this is typically constrained by limited network resources. We employ a time-averaged age metric for characterizing performance of such status update systems. We use system abstractions consisting of a source, a service facility and monitors, with the model of the service facility (physical constraints) a given. While prior work examined first-come-first-served (FCFS) queues, this paper looks at the queue discipline of last-come-first-served (LCFS). We explore LCFS systems with and without the ability to preempt the packet currently in service. For each we derive a general expression for system age and solve for the average age a Poisson source can achieve given memoryless service. Specifically, when preemption is allowed, we evaluate how the source would share the service facility with other independent Poisson sources.