This research seems to indicate they do, at least in certain situations. From the article "Embodiment of Abstract Concepts: Good and Bad in Right- and Left-Handers" (Journal of Experimental Psychology) by Daniel Casasanto [linked to here]:
Whereas right-handers tend to associate right with positive ideas and left with negative ideas, left-handers show the opposite pattern, associating positive attributes like goodness, intelligence, attractiveness, and honesty with the left side of space. Both groups implicitly associate good things more strongly with their dominant side: the side on which they can act more fluently with their dominant hands. These results validate the body-specificity hypothesis. People with different kinds of bodies, who interact with their physical environments in systematically different ways, form correspondingly different mental representations, even in abstract domains.
In a Newsweek article about this research, Sharon Begley suggests:
Memo to restaurant owners: if there are particular dishes you want more customers to order, list them on the right side of the menu.
I hope more research is done on the body-specificity hypothesis, this idea that people with different kinds of bodies (e.g., right- versus left-handedness) think about their worlds differently. Could have some very intriguing applications—beyond restaurant choices.
Note added August 8, 2009: Another article on this research: "Lefty or Righty? A new hold on how we think" (Stanford University News).



