Then there's space, where it gets even more fun, as the relevant frames - the ship, the orbit (or the "centre of gravity" of everything pulling on you) - are completely independent. That is, your orientation doesn't matter for the travel direction. Now, not only "right" and "left" are ambiguous - but also "up", "down", "forward" and "backward".
When in orbit, you have "prograde" and "retrograde" to refer to the velocity vector's direction and its opposite; if we dub that "forward" and "backward", then "radial" and "antiradial" are "down" and "up" (i.e. towards / away from the center of orbited body), and then "normal", "antinormal" for "left" and "right", which you can get from the cross product of "forward" and "up".