Careful examination of 28,460 selected Wide Field and Planetary Camera 2 (WFPC2) long exposures from 1994, 1995, and early 1996 has revealed trails of 96 distinct moving objects. They have been reported to the International Astronomical Union's (IAU) Minor Planet Center for their asteroid database and a few have been identified with known asteroids and used to update their orbits. Most of the objects are new, as they are too faint to show up on ground-based surveys.The trails often show a characteristic curvature due to the parallax induced by HST's orbital motion during the exposures. Using ephemerides for HST, the distance to each object can be directly determined from the parallax contribution to the trail shapes. Based on these distances, constraints on the orbits, and photometry of the trails (16 <V< 24), most of the moving objects appear to be small, main-belt asteroids a few km in diameter. A few are known objects-three are potential Mars crossers. Modern wide-field CCD surveys detect asteroids nearly as faint as these (V< 21), but the corresponding absolute magnitudes are uncertain unless their orbits have been established. The detected objects span the absolute magnitude range 13.6 <H< 19.3 (His the symbol for absolute magnitude, not H-band). Statistics of the detections imply a reservoir of (3.1 ± 0.6) × 105such asteroids within 25° of the ecliptic. We find that the slope of the cumulative distribution of absolute magnitudes follows a power law N ∝ H0.2to N ∝ H0.3over this absolute magnitude range in the three distance ranges defined by the Palomar-Leiden survey. These are significantly shallower slopes than those inferred by the Palomar-Leiden survey or extrapolated from population studies of larger asteroids.