Good question that got me waist-deep in PubMed. It appears that the directionality of myosin motors is due to the angle at which the actin-binding catalytic domain is attached to the neck region. This review by Vale and Milligan, 2000, sums up the "unzippering" of the neck region that contributes the force for the movement (a video from the review adapted for Alberts' textbook is also informative).
Most myosins move towards the plus end of actin, but myosin VI moves towards the minus end. The neck region of myosin VI attaches to the head region at a different angle than conventional myosins and this is the apparent reason for the change in direction preference (see Figure 1 in review by Rodriguez and Cheney, 2000; also Volkmann and Hanein, 2000; Masuda, 2008).
And for your entertainment, an awesome movie of myosin V walking by Kodera et al, 2010 on YouTube.