Planar serpentine antennas disclosed include a generally flat, non-conductive carrier layer and a generally flat radiator of a preselected length and arranged in a generally serpentine pattern that is secured to a surface of the carrier layer. One form of the antenna disclosed that is particularly suited for vehicle transceivers and mounting on a vehicle window in a stick-on fashion has a series of change of direction points characterized by a succession of right angle turns and back folds to obtain substantially the greatest length in the smallest surface area. Another form of the antennas disclosed that are particularly suited for AM/FM radios, stereos, etc. have a sinuous pattern with radiator sections in parallel spaced relation to one another and further are connected at opposite ends in curved back folds. At least one and sometimes a pair of flat ground conductors are secured to a surface of the carrier layer in the same manner as the radiator to optimize the impedance match between a connecting cable and the radiator.