It has long been thought that only symmetric top molecules (or equivalent) can be appreciably oriented in an electric field. This assessment is unduly pessimistic. In molecular beams produced by supersonic expansion, the rotational temperature can be made very low (approximately 1 k). For many diatomic, linear, or asymmetric top molecules, quite substantial orientation can thereby be attained for a large fraction of the beam at accessible field strengths (approximately 100 kV/cm or less). We present model calculations and an experimental design to evaluate the method by observing the fluorescence of photofragments from oriented molecules. Nomograms are provided from which the orientation can be estimated for linear molecules from the dipole moment, rotational constant, rotational temperature, and field strength.