This answer is pulled in its entirety by permission from ThemBid.com

This tutorial was created using Adobe Photoshop CS2. When I first started with Photoshop, many years ago, I remember removing backgrounds manually using the eraser tool. Very tedious, but you can sometimes get good results. Here I will show you how to do remove backgrounds very quickly with good results using Photoshop’s extract feature.

Click here for the GIMP version.

1. Load up your photo. I grabbed the photo for this tutorial from Stock.Xchng.

Here is the original test photo that I will use

2. Filter->Extract… or Alt+Ctrl+X
3. Using the highlighter tool trace the edges of what you want to crop. Use a smaller brush size (around 5) for well defined areas and a larger brush size (around 20) for areas that are less defined like the hair. Use the zoom tool at least once to get a better view. If you have a shaky hand, you may want to use the Smart Highlighting feature.

4. Use the fill tool to specify what areas of the photo you want to extract and click ok.

5. Duplicate and merge the two layers. Cntrl-J then select both layers and then Cntrl-E.
6. Paint in missing drop outs using the History Brush Tool.
7. Use the eraser tool to get rid of any extra stray smudges around the edges.
8. Choose a background and drop it into the photo behind the layer

This technique is very good if you just want to do some quick mockups and get some feedback. If you require better results (so that people will question whether your work is “shopped” rather than just assuming it is) you will need to spend more time in the Extract filter stage perfecting your edges and then extra time during steps 6 and 7.
If possible, do all of the editing with a large, high resolution file and then downsize the final file. This works especially well if the final result will be on a medium where you don’t need a high resolution photo such as a web page.