Four-Star Dragon Ball Hat

The Four-Star Dragon Ball Hat is a hat created by Goku for his son Gohan. In memory of Grandpa Gohan whom his son was named after, Goku attached the Four-Star Dragon Ball onto it.

Overview
Gohan's Hat first appears at the beginning of Dragon Ball Z where it is worn by Gohan. In the anime, Gohan is wearing it when he loses it to a Sabertooth Cat he encounters in the forest. As his father had given him the hat, Gohan chases after the cat crying; though the Sabertooth Cat manages to elude Gohan. Goku soon encounters the Cat wearing the hat and asks it where Gohan is. The cat replies by growling at Goku, leading Goku to ask it again in a more angry tone. This scares the cat, causing it to drop the hat and flee. Goku later returns the hat to Gohan after finding him and the two leave to go visit Goku's friends at Kame House. After introducing Gohan to his friends, Bulma notices the Dragon Ball on Gohan's hat and Goku explains that he found the 4-Star Dragon Ball which was a treasured keepsake he kept in memory of his grandfather who was his son's namesake, so Goku decided to attach it to the hat and gave it to his son.

The hat played an important role when Gohan was kidnapped by Goku's evil older brother Raditz, as Goku realized he could use Bulma's Dragon Radar to track the Dragon Ball on Gohan's hat allowing him to locate where Raditz had taken Gohan. Joining forces with Piccolo, Goku used the Dragon Radar to find the impact site of Raditz's Attack Ball where Gohan was imprisoned, leading to the battle with Raditz. The hat was knocked off of Gohan's head when the raging Gohan broke the Attack Ball, landing outside of the Attack Ball's impact crater, later to be found by Krillin. The Dragon Ball was later removed so it could be used with the other six Dragon Balls to summon Shenron in order to wish Goku back to life after his training with King Kai. The hat does not appear in the manga after this. In the anime it only appears in flashbacks and photographs. It is worn by Gohan in two of the films.

Dragon Ball Z: Dead Zone
Gohan wears the hat in the film as it takes place at least a year before the arrival of Raditz. Once again it plays an important role in the plot as the Dragon Ball attached to it results in Gohan being kidnapped by Garlic Jr.'s henchman who were hunting for the Dragon Balls so Garlic Jr. could use them to obtain Immortality. Gohan wears the hat for a while during his stay at Garlic Jr.'s castle such as when he gets drunk after eating one of the apples, though, the Dragon Ball is later removed and used with the other six Dragon Balls when Garlic Jr. summons Shenron to wish for immortality, though fortunately Goku is able to use the Dragon Radar to find Garlic Jr.'s castle before the Dragon Balls scatter and turn to stone.

Dragon Ball Z: Lord Slug
Gohan wears that hat while hanging out with Piccolo and Icarus at the beginning of the film and when he confronts Lord Slug's soldiers though it is eventually knocked off during the fight and is found by Lord Slug who being a Namekian recognizes it as a Dragon Ball. Slug removes the Dragon Ball and reads Bulma's mind learning about the Dragon Radar which his henchmen use to find the other Dragon Balls so Lord Slug can wish to have his youth restored by Shenron.

Video Game Appearances
In Dragon Ball Xenoverse, Gohan's hat appears as part of one of Kid Gohan's unlockable alternate costume skillsets.

The hat was named Four-Star Dragon Ball Hat in Dragon Ball Xenoverse 2 where it once again appears as part of Kid Gohan's Qipao alternate costume skillset and as an obtainable accessory for the Future Warrior. It is unclear if the Dragon Ball on the hat the Warrior wears is real or not, though its description implies it is a real Dragon Ball. Humorously the Four-Star Shadow Dragon, Nuova Shenron has special dialog with Gohan where he comments on how he used to ride on Gohan's head referring to the time when the 4-Star Dragon Ball was attached to Gohan's hat (it should be noted that the negative energy that spawned Nuova Shenron was already contained within the 4-Star Dragon Ball during the time it was attached to the hat, as it was created when King Piccolo wished for his youth to be restored, thus explaining Nuova Shenron knowledge of the hat).

Trivia

 * It should be noted while the Four-Star Dragon Ball on the hat ultimately allows Goku to find Raditz and his son in the Raditz Saga using the Dragon Radar in both the manga and anime, it should be noted that it unintentionally makes the young Gohan (the hat's owner) a target for anyone searching for the Dragon Balls such as The Three Lords Ginger, Nicky, and Sansho as shown in the Dead Zone film. However it is likely that Goku failed to realize this given his naïve personality and only did so for sentimental reasons as the 4-Star Dragon Ball originally belonged to his adoptive grandfather.
 * Presumably this may be one of the reasons why Gohan never wears his Dragon Ball Hat after the battle of Raditz in the original manga (as Goku may have chosen not to seek out the 4-Star Dragon Ball to recreate the hat due to it potentially putting his family in unnecessary danger in addition to being busy with training for the Androids).
 * Its presence in the Lord Slug film (which is revealed to take place in an alternate timeline in Xenoverse 2), implies that Goku found the 4-Star Dragon Ball and placed it back on the hat for Gohan to wear. The Lord Slug film is that hat's final physical appearance in the films as Gohan only wears his qipao (without the hat) when studying at home in the following film Cooler's Revenge.