twist tie

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A short length of wire encased in a strip of paper, plastic, or foil, designed to be twisted around an item or items as a fastener.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun A metal wire that is encased in a thin strip of paper or plastic and is used to tie the openings of bags, such as garbage bags or bread bags.