Trying to remember the title of a short story about a robot who survives several generations of a family, and at one point stows away on a spaceship. It was an older story — I want to say pre-1970 — part of an anthology. There was some reason why he stowed away. Maybe he was trying to get home? His longevity figured into the plot somehow. He might have been facing obsolescence.
That's "All the Traps of Earth" by Clifford Simak. It was first printed in The Magazine of Fantasy and Science Fiction, March 1960. See http://www.isfdb.org/cgi-bin/title.cgi?41672 for more.
The robot is named Richard Daniel. It served the Barrington family for six hundred years and when the story starts, the family is extinct and the estate -- robot included -- is being sold. The robot stows away on the outside of an interstellar ship and gains psi powers from the experience. He settles on a frontier planet and uses his powers to help people.