Circumstellar accretion disks transfer matter from molecular clouds to young stars and to the sites of planet formation. The disks observed around pre-main-sequence stars have properties consistent with those expected for the pre-solar nebula from which our own Solar System formed 4.5 Gyr ago. But the 'debris' disks that encircle more than 15% of nearby main-sequence stars appear to have very small amounts of gas, based on observations of the tracer molecule carbon monoxide: these observations have yielded gas/dust ratios much less than 0.1, whereas the interstellar value is about 100 (ref. 9). Here we report observations of the lowest rotational transitions of molecular hydrogen (H2) that reveal large quantities of gas in the debris disks around the stars beta Pictoris, 49 Ceti and HD135344. The gas masses calculated from the data are several hundreds to a thousand times greater than those estimated from the CO observations, and yield gas/dust ratios of the same order as the interstellar value.