The detection of terrestrial-sized extrasolar planets from the ground has been thought to be virtually impossible due to atmospheric scintillation limits. However, we show that this is not the case for specially selected (but nevertheless main sequence) stars, namely small eclipsing binaries. For the smallest of these systems, CM Draconis, several months to a few years of photometric observations with 1-m-class telescopes will be sufficient to detect the transits of any short-period planets of sizes >=1.5 Earth radii (RE), using cross-correlation analysis with moderately good photometry. Somewhat larger telescopes will be needed to extend this detectability to terrestrial planets in larger eclipsing binary systems. (We arbitrarily define ``terrestrial planets'' herein as those whose disc areas are closer to that of Earth's than Neptune's i.e., less than about 2.78 RE.) As a ``spin-off'' of such observations, we will also be able to detect the presence of Jovian-mass planets without transits using the timing of the eclipse minima. Eclipse minima will drift in time as the binary system is offset by a sufficiently massive planet (i.e., one Jupiter mass) about the binary/giant-planet barycenter, causing a periodic variation in the light travel time to the observer. We present here an outline of present observations taking place at the University of California Lick Observatory using the Crossley 0.9-m telescope in collaboration with other observatories (in South Korea, Crete, France, Canary Islands, and New York) to detect or constrain the existence of terrestrial planets around main sequence eclipsing binary star systems, starting with CM Draconis. We demonstrate the applicability of photometric data to the general detection of gas giant planets via eclipse minima timings in many other small-mass eclipsing binary systems as well.