We searched for dust or debris rings in the Pluto-Charon system before, during, and after the New Horizons encounter. Methodologies included searching for back-scattered light during the approach to Pluto (phase $sim15^circ$), in situ detection of impacting particles, a search for stellar occultations near the time of closest approach, and by forward-scattered light during departure (phase $sim165^circ$). A search using HST prior to the encounter also contributed to the results. No rings, debris, or dust features were observed, but our detection limits provide an improved picture of the environment throughout the Pluto-Charon system. Searches for rings in back-scattered light covered 35,000-250,000 km from the system barycenter, a zone that starts interior to the orbit of Styx, and extends to four times the orbital radius of Hydra. We obtained our firmest limits using the NH LORRI camera in the inner half of this region. Our limits on the normal $I/F$ of an unseen ring depends on the radial scale of the rings: $2times10^{-8}$ ($3sigma$) for 1500 km wide rings, $1times10^{-8}$ for 6000 km rings, and $7times10^{-9}$ for 12,000 km rings. Beyond $sim100,000$ km from Pluto, HST observations limit normal $I/F$ to $sim8times10^{-8}$. Searches for dust from forward-scattered light extended from the surface of Pluto to the Pluto-Charon Hill sphere ($r_{rm Hill}=6.4times10^6$ km). No evidence for rings or dust was detected to normal $I/F$ limits of $sim8.9times10^{-7}$ on $sim10^4$ km scales. Four occulation observations also probed the space interior to Hydra, but again no dust or debris was detected. Elsewhere in the solar system, small moons commonly share their orbits with faint dust rings. Our results suggest that small grains are quickly lost from the system due to solar radiation pressure, whereas larger particles are unstable due to perturbations by the known moons.