Q:
If nothing can escape from a black hole, then won't the whole universe eventually be swallowed up?
A:
A basic answer to your question is that the universe is a big place. In particular, the size of a region where a particular black hole has significant gravitational influence is quite limited compared to the size of a galaxy. This applies even to massive black holes like the one found in the middle of our galaxy. This black hole has probably already "eaten" most or all of the stars that formed nearby, and stars further out are mostly safe from being pulled in. Since this black hole already weighs a few million times the mass of the Sun, there will only be small increases in its mass if it swallows a few more Sun-like stars. There is no danger of the Earth (located 26,000 light years away from the Milky Way's black hole) being pulled in.
Future galaxy collisions will cause black holes to grow in size, for example by merging of two black holes. But, collisions won't happen indefinitely (because the universe is big and because it's expanding), and so it's very unlikely that any sort of black hole runaway effect will occur.
Revised: September 10, 2008