Voyager 1, that intrepid spacecraft launched in 1977, has entered the last reaches of the solar system (depending on how you define the solar system). What does this mean?
The sun blows a wind of charged particles at speeds of up to 500 miles per second. This solar wind is created by the sun's magnetic field and is responsible for the Earth's auroras. Even out beyond the orbit of Pluto, the solar wind essentially controls all of the magnetic and electric dynamics of the solar system.
As the wind moves outward, it thins out because it needs to fill more space. Eventually the solar wind runs into the winds of other stars and of our galaxy itself. The solar wind abruptly slows way down in a termination shock, which also heats up the wind. The wind piles up, becoming denser (though it is still a far better vacuum than humans can make on Earth!).
Voyager 1 has now definitely crossed this termination shock and entered the heliosheath, a region where the solar wind continues to dominate, but moves more slowly. Eventually, the Voyager probe will cross the "heliopause," where the solar wind will end and the interstellar gases of the Milky Way galaxy will rule.
So, how far away are all these things? Right now, Voyager 1 is about 9 billion miles from the sun, or 94 times the distance from the Earth to the Sun. For reference, Pluto is, on average, 40 times further away from the sun than the Earth. The distance to the heliopause is uncertain, but is thought to be around 110 times the Earth-Sun distance. Voyager 1 should have enough electricity and fuel to communicate with the Earth until the year 2020, at which point it should be almost 150 times the Earth-Sun distance away, or almost 14 billion miles!
But does the heliopause really mark the edge of the Solar System? The heliopause marks the limits of the sun's magnetic influence, but the sun's gravitational pull extends further yet. The Oort Cloud, comets in giant orbits around the sun, may extend out nearly one light year, or six trillion miles. That's over 550 times the distance to the heliopause! Voyager 1, at its current rate of speed, will take almost 18,000 years to reach this distance and become a true interstellar spaceship.