A memory system may include an integrated circuit memory device and a memory controller coupled to the integrated circuit memory device. The integrated circuit memory device may include a memory cell array having a plurality of memory cells, a clock generator configured to generate a clock signal, a plurality of data input/output buffers, and a delay circuit. The plurality of data input/output buffers may be coupled between respective data input/output pads and the memory cell array, and each of the data input/output buffers may be configured to communicate data with the memory cell array responsive to the clock signal with the clock signal being applied to a clock input of each of the input/output buffers. The delay circuit may be coupled between the clock generator and a first one of the data input/output buffers so that the clock signal is delayed by different amounts at clock inputs of the first data input/output buffer and a second one of the data input/output buffers. Moreover, the memory controller may be configured to perform data training. Related methods and memory devices are also discussed.