What are the things on the end of your shoestrings to keep them from unraveling called?

Answer 1

aglets

Answer 2

They're called aglets.
ag·let (āg'lĭt) Pronunciation Key
n.
A tag or sheath, as of plastic, on the end of a lace, cord, or ribbon to facilitate its passing through eyelet holes.
A similar device used for an ornament.


[Middle English, from Old French aguillette, diminutive of aguille, needle, from Vulgar Latin *acūcula, from Late Latin acucula, diminutive of Latin acus, needle; see ak- in Indo-European roots.]

Answer 3

a plain or ornamental metal or plastic sheath covering the end of a shoelace or ribbon is an aglet.