Even though it's considered a "weak" force, gravity basically binds everything in the known universe, from the micro to the macro.
Gravity keeps the earth rotating around the sun and the moon rotating around the earth. But this won't always be the case, at least, in the latter example. Because of the laser fired daily at reflectors placed on the moon by astronauts, we can detect that the moon is gradually moving further and further away from the earth at a rate of a couple of inches a year. This is gradually slowing down the rotation of the earth to the extent that 100 years from now the average day will be a couple of milliseconds shorter than it is now.