Dr. Pulaski doesn't get busy, she gets biz-zay

The basic scuttlebutt is as follows:

1. Gates McFadden was fired after first season because of a personality conflict between her and the head writer. Sexism apparently played a role in this mutual dislike.
2. Diane Muldaur (Pulaski) was brought in to be more of a Bones-esque character. Muldaur reportedly did not like the show too much and never intended to stay on for more than a season. Her character was declared a failed experiment and she was not offered a renewal. Which was cool with her as she went on to LA Law.
3. The writer McFadden had an issue with was fired after season 2 and McFadden was offered the role as Crusher once again.

And now you know the rest of the story.

Cannonically: She died on the way back to her home planet.