Escape velocity is the velocity at which a body must travel before it breaks free of the gravitational pull of a celestial body. It varies widely based on the body's mass. The Earth's escape velocity is 11.186 km/s (25,022 mph or about Mach 37), which can only reached by powerful booster rockets. By comparison, the Space Shuttle's top speed is about 7.6 km/sec, enough to reach Low Earth Orbit but not escape the Earth's gravitational pull entirely.
The escape velocity on Mars' moon Phobos is about 11 m/s, or 25 mph. The body's mean diameter is 11 km (6.8 mi). Its smaller cousin, Demos, with a mean diameter of 6 km (3.7 mi), has an escape velocity of only 6.9 m/s (15 mph), meaning that you could probably jump right off it if you tried hard enough. The gravitational force decreases with the square of the distance, meaning that if a certain distance away from the body the gravity is only half that on the surface, at twice that distance the gravity will be four times less, eight times less, and so on.
Jupiter, the King of the Planets, has an escape velocity of 59.5 km/s (133,100 mph), about 5 1/2 times our own. Despite the size of Jupiter, the velocity is lower than one might think, due to the low density of the planet. Regardless, it would require some powerful rockets to accelerate a payload away from Jupiter's gravitational field.
Perhaps the most famous escape velocity is that of a black hole's — equal to light. Because of its tremendous mass concentrated into a tiny area, nothing can beat the escape velocity of a black hole. The only reasons we know they are there is that they are predicted by stellar evolution models, and infalling gases get superheated, sending out heat and light. It is also known that black holes slowly evaporate through something called Hawking radiation which deals with quantum tunneling effects.
The reason we are so stuck on Earth today is because of its high escape velocity. To spread to the rest of the Solar System and eventually the universe, we must conquer our own gravity cheaply and reliably. This has not yet been achieved. Solutions may involve maglev-assist launches, huge electromagnetic rail guns, or even a space beanstalk.