Muhammad's Child Bride, Aisha, and others inform us about the how much a stolen item must be worth before amputating the thief's hand can be undertaken:

Narrated 'Aisha: The Prophet said, "The hand should be cut off for stealing something that is worth a quarter of a Dinar or more."
Sahih Bukhari 8:81:780, See also: Sahih Bukhari 8:81:781-782, Sahih Muslim 17:4175-4180, and Al-Muwatta 41 7.24b
Narrated 'Aisha: The hand of a thief was not cut off during the lifetime of the Prophet except for stealing something equal to a shield in value.
Sahih Bukhari 8:81:783, See also: Sahih Bukhari 8:81:784-786, and Sahih Muslim 17:4181-4182
Narrated Ibn 'Umar: Allah's Apostle cut off the hand of a thief for stealing a shield that was worth three Dirhams.
Sahih Bukhari 8:81:787, See also: Sahih Bukhari 8:81:788-790, Sahih Muslim 17:4183-4184 and Al-Muwatta 41 7.21b
Narrated Abu Huraira: Allah 's Apostle said, "Allah curses the thief who steals an egg (or a helmet) for which his hand is to be cut off, or steals a rope, for which his hand is to be cut off."
DEBATE QUESTION:  "Do you believe that the "punishment fits the crime" when a thief gets his hand chopped off for stealing an egg, rope, helmet, or shield?"