We propose iterative detection and decoding (IDD) algorithms with Low-Density Parity-Check (LDPC) codes for Multiple Input Multiple Output (MIMO) systems operating in block-fading and fast Rayleigh fading channels. Soft-input soft-output minimum mean-square error receivers with successive interference cancellation are considered. In particular, we devise a novel strategy to improve the bit error rate (BER) performance of IDD schemes, which takes into account the soft \textit{a posteriori} output of the decoder in a block-fading channel when Root-Check LDPC codes are used. A MIMO IDD receiver with soft information processing that exploits the code structure and the behavior of the log likelihood ratios is also developed. Moreover, we present a scheduling algorithm for decoding LDPC codes in block-fading channels. Simulations show that the proposed techniques result in significant gains in terms of BER for both block-fading and fast-fading channels.