If you only need a clean cutout (product shots, profile pictures, quick mockups), you do not have to trace edges by hand anymore. A few things that make the result better:

• Start from a sharp photo with good contrast between subject and background; hair and fur are easiest when the background is plain.
• Export as PNG, not JPG, so the transparency is kept. JPG will turn the empty area white or black.
• Check the edges on both a light and a dark background before using the cutout, since halos only show up on one of them.
• For tricky edges, run the automatic cutout first and only touch up the few spots that are wrong.

For the automatic step, a free browser tool works fine: upload the photo, wait a few seconds and download the transparent PNG. One example (Spanish interface, no signup): More Info

What do you all use for quick background removal: a desktop editor, a plugin or a web tool?