Jack Rollins, a producer and a sharp-eyed talent manager who saw more than a shy gag-writer in Woody Allen and believed that the manic improvisations of Robin Williams would crack up audiences, died on Thursday at his home in Manhattan. He was 100. His daughter Susan Rollins confirmed his death. Mr. Rollins did not just boost fragile young egos. To his clients — who also included Billy Crystal, David Letterman, Lenny Bruce and the team of Mike Nichols and Elaine May, an American pantheon of hilarity — he was a father-confessor, real estate agent, psychiatrist, marriage counselor and financial guru.