What would it be like to fall into a black hole?

The answer depends on a number of things. Black holes (like most objects in the universe) tend to spin, which would make the journey complicated. Your experience would also depend on the black hole's mass.

From National Geographic's "Are We Alone?" special magazine:

With a black hole the mass of an average star, the difference in gravitational force between your head and your feet would tear you apart before you could fall through the event horizon. Ironically, with a much more massive black hole (like the colossal black holes at the centers of galaxies), you might actually pass through the event horizon before gravitational forces would overwhelm you So let's say you dive into one of those, and for simplicity's sake, it isn't spinning. What then?

As you approach the black hole, you notice space is warped around it You might see lensed images of stars and galaxies beyond the black hole. As you get closer, the warping of space allows you to see parts of both sides of the black hole simultaneously.

You won't notice anything as you pass through the event horizon; it's a mathematical boundary.
From your perspective, you'll have no way of knowing that anything special has happened.

As you approach the singularity at the center of the black hole, gravitational forces stretch you out vertically and compress you horizontally. The extreme curvature of space distorts and compresses your view of the universe outside the black hole.

One-tenth of a second before you hit the singularity, you are torn to pieces. All light is rushing toward the singularity, so you can never "see" it coming.

From National Geographic's "Are We Alone?" special magazine: