Context. The mysterious solar system object 133P/(7968) Elst-Pizarro is dynamically asteroidal, yet displays recurrent comet-like dust emission. Two scenarios were hypothesized to explain this unusual behavior: 1) 133P is a classical comet from the outer solar system that has evolved onto a main-belt orbit or 2) 133P is a dynamically ordinary main-belt asteroid on which subsurface ice has recently been exposed. If 1) is correct, the expected rarity of a dynamical transition onto an asteroidal orbit implies that 133P could be alone in the main belt. In contrast, if 2) is correct, other icy main-belt objects should exist and could also exhibit cometary activity. Aims. Believing 133P to be a dynamically ordinary, yet icy main-belt asteroid, I set out to test the primary prediction of the hypothesis: that 133P-like objects should be common and could be found by an appropriately designed observational survey. Methods. I conducted just such a survey -the Hawaii Trails Project -of selected main-belt asteroids in a search for objects displaying cometary activity. Optical observations were made of targets selected from among the Themis, Koronis, and Veritas asteroid families, the Karin asteroid cluster, and low-inclination, kilometer-scale outer-belt asteroids, using the Lulin 1.0 m, small and moderate aperture research telescope system (SMARTS) 1.0 m, University of Hawaii 2.2 m, southern astrophysical research (SOAR) 4.1 m, Gemini North 8.1 m, Subaru 8.2 m, and Keck I 10 m telescopes. Results. I made 657 observations of 599 asteroids, discovering one active object now known as 176P/LINEAR, leading to the identification of the new cometary class of main-belt comets (MBCs). These results suggest that there could be ∼100 currently active MBCs among low-inclination, kilometer-scale outer-belt asteroids. Physically and statistically, MBC activity is consistent with initiation by meter-sized impactors. The estimated rate of impacts and sizes of resulting active sites, however, imply that 133P-sized bodies should become significantly devolatilized over Gyr timescales, suggesting that 133P, and possibly the other MBCs as well, could be secondary, or even multigenerational, fragments from recent breakup events.