General antonyms:
* Worthless
* Valueless
* Cheap
* Common
* Ordinary
* Insignificant
* Trivial
* Meaningless
Antonyms emphasizing lack of value:
* Trashy
* Junk
* Rubbish
* Dross
Antonyms emphasizing lack of rarity:
* Abundant
* Plentiful
* Commonplace
Antonyms emphasizing lack of emotional importance:
* Unimportant
* Indifferent
* Disregarded
Antonyms emphasizing lack of physical beauty:
* Ugly
* Unattractive
* Plain
The best antonym for "precious" will depend on the specific context of your sentence.