If the background is a solid colour you can sometimes get away with using the magic wand but for best results you need to use the polygon lasso tool.
If the image is very complicated (hair, fire, ect) it is often easyier to use blend modes as lassoing would look too jagged.
For example to add a firey explosion over an image you would probably have to screen it, which basically makes black (or white i think) bits clear...
Screened:
If you used a magic want or lasso it would look crappy.
Images which have been lassoed can be better blended by using artifical multisampleing (copy the image, move behind original and apply a blur) or things such as zoom blurs can create an artifical depth of field type effect bleding the image into the background...
As you can see in the circled bits it appears asthough it is part of the image as apposed to a flat picture stuck ontop.
Photoshop or Fireworks both work great.