Cold molecular clouds are the birthplaces of stars and planets, where dense cores of gas collapse to form protostars. The dust mixed in these clouds is thought to be made of grains of an average size of 0.1 micrometer. We report the widespread detection of the coreshine effect as a direct sign of the existence of grown, micrometer-sized dust grains. This effect is seen in half of the cores we have analyzed in our survey, spanning all Galactic longitudes, and is dominated by changes in the internal properties and local environment of the cores, implying that the coreshine effect can be used to constrain fundamental core properties such as the three-dimensional density structure and ages and also the grain characteristics themselves.