It depends what you want to do with the image. If you actually want to alter the image, you cannot do that in a vector program like corel or illustrator. Illustrator does have the clipping mask function as well though.Don't waste time in photoshop. I've discovered that using Corels clipping mask works the best. You get much finer edges and it's easier to manipulate. I don't know if Illustrater is the same but you might try that too.
I usually use the eraser tool in photoshop. I zoom in one the image, and very carefully trase around the object. Once you have erased around the image, make sure that the image is on its own layer...not the background. Then you can add layers, and chenge the background however you want.