[html] <button> vs. <input type="button" />. Which to use?

Quoting the Forms Page in the HTML manual:

Buttons created with the BUTTON element function just like buttons created with the INPUT element, but they offer richer rendering possibilities: the BUTTON element may have content. For example, a BUTTON element that contains an image functions like and may resemble an INPUT element whose type is set to "image", but the BUTTON element type allows content.