George Hamilton, now appearing in “Godfather III,”...

George Hamilton, now appearing in “Godfather III,” visits the Stones on The Donna Reed Show (Sunday at 9:30 p.m. on Nickelodeon).

Casey Kasem hosts a New Year’s Eve countdown of the most memorable episodes of the old series that are rerun on Nick at Nite and offers behind-the-scenes stories and a few long-distance dedications on the second annual Nick at Nite’s Top Rerun Countdown (Monday 11:30 a.m.-midnight on Nickelodeon).

TBS begins airing a month of unedited versions of The Andy Griffith Show (Tuesday at 3:35 p.m. on TBS), complete with the epilogues-the final two- to three-minute wrap-ups at the end often sliced out to make room for commercials-and all program cuts restored. TBS also repeats the anniversary special 30 Years of Andy: A Mayberry Reunion (Tuesday at 12:15 p.m. on TBS).

The late Gloria Grahame and Shirley Knight guest on The Fugitive (Tuesday at 2 p.m. on A&E;) in an episode in which Richard Kimble is caught in a bitter family struggle.

A pre-”Dallas” Barbara Bel Geddes and a post-”The Day the Earth Stood Still” Michael Rennie guest on Alfred Hitchcock Presents (Wednesday at 11 p.m. on Nickelodeon) in an episode about a couple who get lost in the fog during a sailboat ride in San Francisco Bay.

Oscar-winner Ed Begley plays a law professor who stages a mock trial to prove Kimble’s innocence on The Fugitive (Friday at 2 p.m. on A&E;).

Desi Arnaz Jr. appears as himself on The Brady Bunch (Friday at 2:35 p.m. on TBS) when Marcia’s diary, in which she confides her deep feelings for the son of Lucille Ball and Desi Arnaz, is accidently given away.

Dame Wendy Hiller stars on Alfred Hitchcock Presents (Friday at 11 p.m. on Nickelodeon) as a private girl’s teacher who becomes involved in blackmail.