Fievel's hat is an important plot element in An American Tail. Although an inanimate object, it impacts the plot and becomes an important part of Fievel's identity. It is a Mousekewitz family heirloom, passed down through the male side of the family.
Fievel's hat is blue and oversized, with large yellow buttons on either side and a black bill. It is technically a Russian Kasket cap, worn by many Russian Jews in the 1800's, similar in style to the Greek Fisherman's cap and the Dutchboy cap. It's shade of blue varies in the sequels. On the inside it is red.
An American Tail
At the beginning of the film, Papa presents the hat to Fievel as a Hanukkah gift. He explains that it belonged to his father, and his father's father, meaning it originally belonged to Fievel's great-grandfather. If they have human lifespans (as is implied in the series), this would date the hat to the 1700's. The hat is too big for Fievel at first.
The hat becomes Fievel's only memento from his family when he is swept overboard on the boat to America, and lost in New York. Fievel carries it with him, sometimes tucking it into the back of his belt. He loses the hat during the fire at the pier, and it is found by Bridget. Later when she shows it to Fievel's mother, it proves to them that Fievel is alive.
At the end of the film, when Fievel is reunited with his family, his Papa gives him back the hat, and it finally fits (thanks to Fievel propping it up with his ears). This is seen as a sort of coming-of-age moment for Fievel.
A video game adaptation, An American Tail: The Computer Adventures of Fievel and His Friends, stated that the hat is "endowed with special properties that will help him in life".
Fievel Goes West
In An American Tail: Fievel Goes West, Fievel is bizarrely able to pull his hat inside out and make it become a white cowboy hat. He keeps it this way for the majority of the movie, starting from when he decides to stand up to a cat attack in New York. The hat seems to bring him more courage in this state. At the end of the film, when he speaks to Wylie Burp, Fievel learns that he can be a hero just by being himself. He then turns his hat back to its normal state, perhaps symbolizing that he is now comfortable with his identity and no longer wishes to be something he's not. In its cowboy hat state, it represented what Fievel wanted to be, not who he really was. It is possible he simply imagined it as a cowboy hat.
In its natural state, the hat looks somewhat different from the first film, with a dark blue button at the top.
In Fievel's American Tails Fievel's hat is always a white cowboy hat, and is never seen in its natural state, save for in two old family portraits in the opening intro.
Direct to Video sequels
Fievel is rarely hatless in An American Tail: The Treasure of Manhattan Island and An American Tail: The Mystery of the Night Monster. The hat plays no substantial role in the plots, though in the third movie Tony playfully snatches Fievel's hat and runs away with it, only to trip over a fruit wagon. The hat is back to looking like it did in the first film, but it is a darker shade of blue in these movies.