Characterization Marches On: He and Barney are cousins in the first two episodes, something that isn't brought up again; also, for much of the first season, Griffith played Andy as more of a country bumpkin than the straight man role he played in later episodes.
Flanderization: Andy being the Only Sane Man in Mayberry becomes more and more obvious, especially in the last three seasons, almost to the point where it seems he harbors some contempt for the Eccentric Townsfolk around him.
This was originally planned to be reversed, with Barney being the Straight Man to Andy's Wise Guy. However, the creators (and Griffith himself) was quick to realize that the show was funnier with Andy as the Straight Man.
Happily Married: Andy gets married to Helen in the pilot of Mayberry R.F.D.
Non-Action Guy: In WWII, at least, in contrast to Andy. Barney was never allowed to leave his post in office as a file clerk, while Andy was stationed in France.
Official Couple: With Thelma Lou at first, but the two call it quits when he leaves Mayberry. In Season 6's "The Return of Barney Fife", Barney discovers Thelma Lou has married Gerald Whitfield. But, in 1986's TV movie Return to Mayberry, the couple end up getting officially married.
Small Name, Big Ego: Ignoring all that happens under his nose, Barney considers himself an expert lawman, as well as a specialist on women, singing, history, etc. Andy regularly lets Barney carry on as he pleases, although he only allows him a single bullet in his gun for prime safety reasons.
All Women Want Bad Boys: In the early seasons, Aunt Bee has romances with several men that turn out to be complete jerks. Averted in the color era, when she finds happiness with respectable gentlemen such as a professor and a congressman.
Parental Substitute: For Opie's mother. In the first episode, Opie was originally not too happy with accepting another mother figure into the household, but he warmed up to Aunt Bee by the end of the episode and they became instant friends.
Official Couple: After Barney leaves Mayberry, she ends up marrying Gerald Whitfield, and the episode "The Return of Barney Fife" in Season 6 serves as her last appearance on the show. However, she does return for the 1986 TV movie Return to Mayberry, where she and Barney end up getting married.
You're Just Jealous: In the episode where Andy and Barney help a friend of theirs find a bride and he selects Thelma Lou as the girl he wants to marry, Thelma Lou claims this is the reason Barney is so jealous, although she never wanted to marry anyone else in the first place, and she and Barney get back together at the end of the episode.
Catch-Phrase: Not catch phrase, per se, but he did have a habit of asking, "Huh?" after a long succession of questions.
Chuck Cunningham Syndrome: He disappeared without a trace after eleven appearances in Season 6. In the 1986 TV movie Return to Mayberry, it is mentioned that he became Sheriff of Mayberry after Andy left, and remained at that post until his death.
Howard Sprague (Jack Dodson)The county clerk who officially debuts in Season 6's "The County Clerk" episode.
15 Minutes of Fame: He bowls a perfect 300 game at the bowling alley, only to be overlooked by his teammates who are more upset about Andy calling off the bet.
Mama's Boy: He has a close relationship with his mother.
My Beloved Smother: His domineering mother, who objects to Howard joining the local lodge for fear that he might become a gambler, when the "card games" that take place are just gin rummy and cribbage-type games instead of the "big games" such as poker and blackjack.