Sampling is an expensive network resource, because switches and routers are able to sample only a small fraction of the traffic they receive. Modern switches and routers perform uniform packet sampling, which has several major drawbacks: 1) the same flow might be unnecessarily sampled multiple times in different switches; 2) all the flows traversing a switch whose sampling module is activated are sampled at the same rate; and 3) the sampling rate is fixed, even if the volume of the traffic changes. For the first time, we propose a sampling-on-demand monitoring framework. The proposed framework, presented as a component of software defined network (SDN), adds a sampling management module to the SDN controller. This module allows the controller to determine the sampling rate of each flow at each switch, according to the monitoring goals of the network operator, while taking into account the monitoring capabilities of the switch. As part of the proposed framework, the paper defines a new optimization problem called sampling allocation problem, which has to be solved by the sampling management module in order to maximize the total sampling utility. The paper presents online and offline algorithms for solving this problem. It also presents three real network management applications, executed over Mininet, which are shown to significantly benefit from the proposed framework.