After the completed part has been modeled, you options for moving its origin are reduced but not impossible.
If you need (or want) the origin of the part to be in a different location, it can only be moved via changing the relationship of the initial sketch or sketches (in the case of a loft or sweep) and possibly the feature (in the case of a boss-extrude) to the part origin.
I.E.
Insted of placing the origin on the edge or corner of the initial skecth, place the sketch around the origin and dimension to it or place it away from the origin.
Also , as in a cut extrude, extruding MidPlane or offset will place the origin accordingly.
But these things should normally be thought out before the initial modeling begins.
Remember...
"If you don't use your head,
your going to have to use your feet."