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A Darboux transformation is constructed for the generalized Hirota-Satsuma coupled KdV system and the result is compared with the recent work of Geng and his collaborators [X. G. Geng et al., Phys. Rev. E 79, 056602 (2009) and X. G. Geng and G. L. He, J. Math. Phys. 51, 033514 (2010)]. It is shown that our Darboux transformation may be applied to three interesting reductions of the general system. In addition, the iteration of this Darboux transformation is worked out, and some solutions to the associated systems are obtained. [ABSTRACT FROM AUTHOR]