Dielectric elastomers are used for electromechanical energy conversion in actuators and in harvesting mechanical energy from renewable sources. The electrical breakdown strength determines the limit of a dielectric elastomer for its use in actuators and energy harvesters. We report two experimental configurations for the measurement of the stretch dependence of the electrical breakdown strength of dielectric elastomers, and compare the electrical breakdown fields for compliant and rigid electrodes on the elastomer. We show that the electrode configuration strongly influences the electrical breakdown field strength. Further, we compare the stretch dependent dielectric function and breakdown of the acrylic elastomer VHB 4910™ from 3M™, and of the natural rubber ZruElast™ A1040™ from Zrunek rubber technology. While the dielectric permittivity of VHB decreases with increasing stretch ratio, the dielectric constant of rubber is insensitive to stretch. Our results suggest natural rubber as a versatile material for dielectric elastomer energy harvesting.