Recently, a new paradigm for cognitive radio networks has been advocated, where primary users (PUs) recruit secondary users (SUs) to cooperatively relay the primary traffic and in return grant the SUs the right to access the channel. However, all existing studies on such cooperative cognitive radio networks (CCRNs) operate in the temporal domain only, which limits the performance of both PUs and SUs. On the other hand, multiple-input-multiple-output (MIMO) enables transmission of multiple independent data streams in the spatial domain to improve capacity. Taking advantage of the MIMO technique in CCRNs is an unexplored area that we investigate in this paper. We propose a novel MIMO-CCRN framework, which enables the SUs to utilize MIMO techniques to cooperatively relay the traffic for the PUs, while concurrently accessing the same channel to transmit their own traffic. Specifically, we consider two typical network scenarios. For the case of a general PU link and multiple SUs, we provide theoretical analysis for the link rates and then formulate an optimization model based on a Stackelberg game to maximize the utilities of PUs and SUs. In addition, we extend our analysis to a practical cellular network with multiple MIMO-empowered femtocells, and provide an algorithm to find a stable matching of the PUs and SUs. Evaluation results show that high utility gains are achieved by both PUs and SUs by leveraging MIMO spatial cooperation in our proposed framework.