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Spoilers (2)
Originally Klaus was going to be French and named François. When Dee Bradley Baker auditioned he told the producers that his French wasn't very good and that he would read the lines in German instead, they liked his performance so much they retooled him so he was German instead.
In some establishing shots of the Smith house, a yellow ribbon can be seen tied around a tree, which represents the support of soldiers during wartime and their safe return home.
Steve's friend Snot is based on Booger from Revenge of the Nerds (1984) and is voiced by Curtis Armstrong, who played Booger.
The Season 4 openings changed from different newspaper headlines to Roger in a new disguise at the end.
Steve's original design was much geekier and gawky and he was voiced by Ricky Blitt. Halfway through production, his voice actor changed to Scott Grimes and his design was made to be more attractive, so he would be less comparable to Neil Goldman from Family Guy (1999). This design is a caricature of one of the series creators, Mike Barker.
In American Dad!: Francine's Flashback (2005), we find out that Francine was 20 in 1985. We can draw from this that Francine was born in 1965, and that in the cartoon she is around 40 years old. This is confirmed in American Dad!: Tears of a Clooney (2006), in which it is Francine's 39th birthday.
Fox showed a viewer discretion warning before airing American Dad!: Threat Levels (2005) due to cartoon nudity.
Beginning with season four, in the opening sequence, you can see Barry, Toshi, and Snot looking into an adult store.
The series was partially inspired by All in the Family (1971).
Klaus makes many mentions of being older than he is. One episode he talks about "Berlin in '38". However, he was abducted during the winter olympics somewhere between 1986-1988.
Avery, who is played by Patrick Stewart, also appears in the Family Guy episode "Not All Dogs Go to Heaven," not as Avery but as Patrick Stewart himself.
The Japanese pop song in season 5 episode 12 "may the best Stan win" is "Monochrome Effect" by the Japanese group Perfume.
Hayley says in American Dad!: Stan Knows Best (2005) that she is 18 years old. Based on this information, we can assume that she was born in either 1986 or 1987 (depending on what month her birthday is in.)
The headline of the Langley Falls Post that Stan reads in the opening credits is different in every episode.
The uniformed officer in the Underdog Productions logo at the end says something different in every episode. (Not unique, just out of a small assortment.) In the season 7 finale, he was given a speaking role as Steve's imaginary friend "Pedro".
The final frame of the introduction was changed for seasons beyond the first. At the end of the credits in the first season, all that could be seen was a big "American Dad!" logo in front of the American Flag. In all subsequent scenes, this logo was shrunk to fit the names to the series creators on the same screen.
In some episodes, the opening sequence is shortened severely, and the final few seconds (the flag and the accompanying "Good morning, USA!") of animation is all that remains.
Spoilers
Stan is actually dead as shown in Raptures Delight at the end of the episode he is seen in heaven walking through a door to his family and the episode ends