So why is it useful to study gravity? Aside from the obvious fact, that it keeps you "down to Earth", it affects a lot of other things. We have already mentioned binary stars, the solar system and the orbits of the planets, the moon's orbit, and galaxies and clusters of galaxies. Why not think about the whole universe? We know that the "edge" of the universe is expanding at the speed of light. A fundamental question is, will it expand forever, or will it start to contract at some point in time? If it were to contract, then it must be bound by gravity: there would be enough mass inside the universe to pull itself together, and to put a limit on it's expansion. One of the goals of astronomers these days is to try to estimate how much mass there is in the universe, so that they can answer this question.
Gravity is also important in keeping our atmosphere from drifting away. Without the atmosphere, we would not survive. You are probably also aware of how the moon's gravitational pull on the Earth causes our tides. In fact, the shape of the solid Earth is also slightly modified by the moon's gravitational pull. In space, any gravitational interaction between two objects will have a "tidal" effect, whether they are solid, liquid, or gaseous objects. In fact, in a binary star system, one star often "leaks" some of it's gas to the other star, because of these tidal effects.
We rely on a detailed knowledge of gravity to put satellites around the Earth, so that we can have the luxury of TV and e-mail, etc. Physicists are employed to calculate the exact direction and magnitude of the velocity that must be given to a satellite, so that it will stay in it's orbit around the Earth.
Similarly, when we send space probes like the Galileo and the Voyager crafts into space, we use the gravity of other planets and moons to speed up our space probes. This is called "slingshotting", and it works because we calculate the path of the probe so that it will pass close to a planet, but so that it will have enough kinetic energy to not get caught in an orbit around the planet. As it accelerates toward the planet, it gains kinetic energy, so it will reach it's final destination faster. Below is a diagram of the path of Galileo, a space probe sent to examine Venus and Jupiter.
You have probably noticed that most large objects in space are essentially spherical: stars, planets, moons are almost always spheres. This is because they are held together as masses by gravity, and the gravitational field is strongest closer to the centre of the mass. If a large object is spherical except for, say, one lump or mountain on one side, the mountain will slowly crumble over time, so that it's rocks can move to a more stable position, with a lower gravitational potential energy, closer to the centre. Eventually, it will change into a sphere. So the erosion, landslides, avalanches, and rockfalls that you see in the mountains, they all have gravity to blame.