There are two final things at play here, and the first is the elastic collision. An elastic collision occurs when two objects run into each other, and the combined kinetic energy of the objects is the same before and after the collision. Imagine for a moment a Newton's cradle with only two balls. If Ball One had 10 joules of energy and it hit Ball Two in an elastic collision, Ball Two would swing away with 10 joules. The balls in a Newton's cradle hit each other in a series of elastic collisions, transferring the energy of Ball One through the line on to Ball Five, losing no energy along the way.
At least, that's how it would work in an "ideal" Newton's cradle, which is to say, one in an environment where only energy, momentum and gravity are acting on the balls, all the collisions are perfectly elastic, and the construction of the cradle is perfect. In that situation, the balls would continue to swing forever.
But it's impossible to have an ideal Newton's cradle, because one force will always conspire to slow things to a stop: friction. Friction robs the system of energy, slowly bringing the balls to a standstill.
Though a small amount of friction comes from air resistance, the main source is from within the balls themselves. So what you see in a Newton's cradle aren't really elastic collisions but rather inelastic collisions, in which the kinetic energy after the collision is less than the kinetic energy beforehand. This happens because the balls themselves are not perfectly elastic -- they can't escape the effect of friction. But due to the conservation of energy, the total amount of energy stays the same. As the balls are compressed and return to their original shape, the friction between the molecules inside the ball converts the kinetic energy into heat. The balls also vibrate, which dissipates energy into the air and creates the clicking sound that is the signature of the Newton's cradle.
Imperfections in the construction of the cradle also slow the balls. If the balls aren't perfectly aligned or aren't exactly the same density, that will change the amount of energy it takes to move a given ball. These deviations from the ideal Newton's cradle slow down the swinging of the balls on either end, and eventually result in all the balls swinging together, in unison.
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