Can things truly go in a "straight line" when traveling in space?

Odd question maybe?

Pretty much everything in space has gravity and an orbit of some sort. Things travel in a circular(ish) path around the earth, the sun, the galaxy's center and so on.

So if we wanted to send something out of a particular side of the galaxy toward a target in deep space would we be able to point and shoot or would we have to do some kind of calculation to compensate for rotation?

PS - Please forgive the lack of proper technical terms.

EDIT: terrible illustration of what i'm talking about. Assuming you aim down the blue dashed line, would it actually end up following the other path?