I'm surprised that none of the answers so far have touched on the actual source of the distinction.
The rule is: ください when it attaches to the te form of a verb, and 下さい otherwise. That's why 下さい is used in requesting an item, because it's not being used after the te form of a verb (それを下さい). The same goes for other verbs that attach to the te form... the general rule is to write it in kana even if you would write it in kanji if it were standing alone. For instance, if you were to say "I'm getting bored of my job", the preferred way to write it is 仕事に飽きてきている, not 飽きて来ている.
In practice, this rule is often ignored and ください and 下さい are completely interchangeable. In fact, I've seen one page of a manga that was written entirely in kana except for 下さい, despite it being used with the te form.