This is why the earth has high and low tides. The parts of the earth closer to the moon feel a stronger gravitational force from the moon than the parts further away. This causes the oceans to "bulge" and the tides to rise or fall in different parts of the earth. (Again, see the above picture.)
Ripping Objects Apart.
If tidal forces are strong enough, they can actually do more then make the object bulge, they can rip the object apart. Perhaps the most classic example of this is the Comet Shoemaker-Levy 9.
This comet got too close to Jupiter in 1994 for it own good. The picture above this section is an actual photograph of how the comet was ripped apart into a string of pearls. As you can see tidal forces can be strong enough to cause a lot of damage.
The picture to the above right in this section shows the impacts on Jupiter when this string of pearls was finally brought in by gravity.
The picture to the low left of this section shows a crater structure on Ganymede (On of Jupiter's moons) that scientists believe was caused by an object like the above comet that was similarly ripped into a string of pearls.
Ripping Planets Apart.
Some planets come too close to their host star. When the planets are gaseous like Jupiter, the star can suck in gases through tidal forces. In this way the planet slowly gets "eaten". This is also called accretion.
As reported by Scientific American, astronomers have recently found a planet eaten by the host star.
The giant planet WASP 12 b, discovered in 2008, orbits its star at the uncomfortably close distance of only about 3.4 million kilometers... the planet so close to its star, that WASP 12 b is likely losing mass rapidly to its star... [a] group modeled WASP 12 b's mass loss, finding that it gives away roughly one ten-millionth of its total mass each year... Given WASP 12 b's heft, some 1.4 times the mass of Jupiter, that would mean that the scorching world loses as much mass in just seven years as is contained in all of Earth's oceans.The picture to the right demonstrates this planet being devoured.