Conventional gel electrodes are widely used for biopotential measurements, despite important drawbacks such as skin irritation, long set-up time and uncomfortable removal. Recently introduced dry electrodes with rigid metal pins overcome most of these problems; however, their rigidity causes discomfort and pain. This paper presents dry electrodes offering high user comfort, since they are fabricated from EPDM rubber containing various additives for optimum conductivity, flexibility and ease of fabrication. The electrode impedance is measured on phantoms and human skin. After optimization of the polymer composition, the skin-electrode impedance is only ~10 times larger than that of gel electrodes. Therefore, these electrodes are directly capable of recording strong biopotential signals such as ECG while for low-amplitude signals such as EEG, the electrodes need to be coupled with an active circuit. EEG recordings using active polymer electrodes connected to a clinical EEG system show very promising results: alpha waves can be clearly observed when subjects close their eyes, and correlation and coherence analyses reveal high similarity between dry and gel electrode signals. Moreover, all subjects reported that our polymer electrodes did not cause discomfort. Hence, the polymer-based dry electrodes are promising alternatives to either rigid dry electrodes or conventional gel electrodes.