We develop several novel signal detection algorithms for two-dimensional intersymbol-interference channels. The core in all these schemes is a modified one-dimensional maximum aposteriori (MAP) detection algorithm that operates over single and multiple rows providing a balanced performance vs. complexity tradeoff. We explore 2-D iterative algorithms that operate by feeding extrinsic information from multi-row/column detectors in a turbo fashion. Multi-row/column MAP detection using 2D turbo-processing yields more than 2 dB signal-to-noise ratio (SNR) gain compared to a non-iterative multi-row detector over the additive white Gaussian channel and within 0.1 dB of the ML estimate.