They first showed up in the 1975 Fourth Doctor story Terror of the Zygons. Despite being in one four-parter in the old series in which they pretty much just stomped around being genero-evil, everyone likes to pretend they're iconic.
The Zygons originate from the planet Zygor and have shape-shifting abilities allowing them to replicate the appearance of another being, but
they must keep the subject alive in order to use its body print HA HA MOFFUCKED HARNESSED AGAIN.
The 50th Edit
Need more Zygons? Try Zygon: When Being You Just Isn't Enough.