This is a quick, easy way that I've found to remove a white background:
1) Use the Quick Selection Tool (w) and paint around the inside of the object that you wish to isolate from its background. You might need to go in and manually deselect some areas, by holding down ALT while you paint.
2) Click on Refine Edge at the top of your screen and adjust your settings, to achieve a desired selection edge. These are the settings that I used, but yours will likely be different:
Update: in newer versions of PS, this has been restructured into "Select and mask..."
3) Once you're happy with how the selection looks, click on Add a Layer Mask at the bottom of your Layers Palette:
You've now converted your white background to transparent, while also maintaining the ability to reverse and/or edit any of your steps in the previous steps through editing the mask you've created.