The outage performance of multiple-input multiple-output (MIMO) technique has received intense attention in order to ensure the ultra-reliability requirement for broadcasting systems. In this article, the outage probability at high signal-to-noise ratio (SNR) is asymptotically studied for MIMO channels to thoroughly investigate the transmission reliability. To fully capture the spatial correlation effects, the MIMO fading channel matrix is modelled according to three types of Kronecker correlation structure, i.e., independent, semi-correlated and full-correlated Rayleigh MIMO channels. The outage probabilities under all three Kronecker models are expressed as weighted sum representations of generalized Fox's H functions. The tractable results empower the asymptotic outage analyses, which are conducted not only to reveal helpful insights into understanding the behavior of fading effects, but also to offer useful design guideline for MIMO configurations. Particularly, the asymptotic outage probability is proved to be a monotonically increasing and convex function of the transmission rate. In the absence of the channel state information (CSI), the transmitter tends to equally allocate the total transmit power among its antennas to enhance the reception reliability especially in high SNR regime. In the end, the analytical results are validated through extensive numerical experiments.