The paper describes highly-sensitive passive electric potential sensors (EPS) for non-contact detection of multiple biophysical signals, including electrocardiogram (ECG), respiration cycle (RC), and electroencephalogram (EEG). The proposed EPS uses an optimized transimpedance amplifier (TIA), a single guarded sensing electrode, and an adaptive cancellation loop (ACL) to maximize sensitivity (DC transimpedance $=150$~G$Ω$) in the presence of power line interference (PLI) and motion artifacts. Tests were performed on healthy adult volunteers in noisy and unshielded indoor environments. Useful sensing ranges for ECG, RC, and EEG measurements, as validated against reference contact sensors, were observed to be approximately 50~cm, 100~cm, and 5~cm, respectively. ECG and RC signals were also successfully measured through wooden tables for subjects in sleep-like postures. The EPS were integrated with a wireless microcontroller to realize wireless sensor nodes capable of streaming acquired data to a remote base station in real-time.