Monkey D. Luffy may be young and dimwitted at times, but he is also very kind and lovable, and he happens to be one of One Piece's best fighters. In order to be a captain you need to be strong, but what makes Luffy a true leader is the fact that he will do anything to help people in need, especially his friends.
Luffy wanted to become a pirate at age seven after meeting Shanks and the Red Hair Pirates, and he later made a pact with his foster brothers, Ace and Sabo to set sail when they each turned 17. Luffy was the last one to leave their island home, and when he got into his little boat, he immediately started looking for ten crewmates.
Every pirate crew needs a first mate, and for the Straw Hats that's Zoro-a green-haired man who dreams of becoming the world's greatest swordsman. When Luffy met Zoro, the swordsman was tied to a pole-where he was serving a 30-day sentence for killing a wolf that belonged to the son of a corrupt Marine Captain. The wolf was attacking a little girl at the time, and Zoro agreed to be tied up to gain amnesty. As a bounty hunter, Zoro rejected Luffy's initial invitation to join his crew, but that changed when he learned that Luffy attacked the Captain's son who planned on executing Zoro instead of freeing him.
Nami was the crew's third official member, and the Straw Hat navigator first met Luffy and Zoro while she was stealing a treasure map from Buggy the Clown. During this arc, Luffy saves Nami from Buggy, an act which leads to her joining the crew.
Later during the Arlong Park Arc, Nami "betrays" the Straw Hats by revealing that she was part of Arlong's crew all along, but we later learn that she was forced to join the crew to save herself and her village. Once Arlong betrays her, Luffy, Zoro, Sanji, and Usopp decide to save her and the village themselves, thus solidifying her allegiance to the Straw Hats.
Usopp is pretty cowardly at times, but when push comes to shove he can hold his own against certain enemies. The young Straw Hat crew met Usopp in Syrup Village, and they helped him to defend his friend/love interest Kaya from Kuro, a pirate captain who was plotting to kill her and steal her inheritance.
After Luffy and Zoro saved Usopp and Kaya from certain death, he decided to help them fight Kuro's crew, and this battle caused Usopp to find the courage he needed to set sail and become a pirate like his father. When Luffy invited him to join his crew, he provided the Straw Hats with their Jolly Roger and first ship.
Before it was revealed that Sanji was a member of the infamous Vinsmoke family, One Piece fans knew him as "Black Leg" Sanji-the former sous chef of the seafaring Baratie restaurant. This is where the Straw Hats met their future cook.
Sanji ended up joining the crew after Luffy helped defend the restaurant from Don Krieg, an infamous East Blue pirate. When Luffy fell into the ocean after the fight, Sanji jumped in to save him. The other Baratie chefs later convinced Sanji to join the Straw Hats so he could fulfill his dream of finding the All Blue, a part of the ocean that contains every fish a chef would ever want.
Chopper is the crew's doctor, and he dreams of one day becoming a doctor who can cure any disease. He also happens to be a reindeer who ate a devil fruit that turned him into a human hybrid.
The crew met Chopper on Drum Island, and when Nami invited him to join them he refused due to his mistrust of humans. Luffy defeats Wapol-the former king of the island who killed Chopper's mentor and desecrated his memory. Chopper declines to join the crew yet again, but he changed his mind after remembering how his mentor wanted him to set sail to see the world in order to broaden his medical knowledge.
As a child, Robin witnessed the destruction of her home at the hands of the World Government, and she has been on the run ever since. The Straw Hats met Robin during the Alabasta Arc, where she was originally an antagonist as she initially served as the second in command of Crocodile's criminal organization, Baroque Works.
Crocodile eventually betrays Robin and leaves her for dead, but Luffy ends up saving her life, which is why she appears on the Straw Hats' ship at the end of the arc and asks to join them. Luffy agreed, thus making her the crew's archaeologist.
Franky was the eighth person to join the Straw Hats, and this happened during the Water 7 Arc. This cyborg is the crew's shipwright, and he actually started off as "villain" who stole all of the Straw Hats' gold.
Franky ends up getting kidnapped by CP9 - one of the World Government's covert factions - and when the Straw Hats follow CP9 to Ennies Lobby to rescue Robin, Franky escapes and agrees to help them. Once everyone is safe, Franky reveals that he used the crew's money to buy the wood from the Adam tree (the strongest kind of wood in the One Piece world), which he used to build the Thousand Sunny, the Straw Hats' new ship. He joined them in order to sail around the world on a ship made from this wood.
Luffy wanted a musician for a long time, and he finally got his wish when the crew met Brook during the Thriller Bark Arc. When Brooke was alive, he ate a devil fruit which amplified his soul to the point that he could resurrect himself but by the time he found his body, just a skeleton remained. Every member of the crew was terrified of Brook at first, except for Luffy who invited him to join the crew immediately, but he declined because he could not venture out in sunlight thanks to his shadow being stolen. Luffy and the crew succeeded in retrieving his shadow, but he did not join the crew until he learned that an old friend who was waiting for him to return was still alive.
Jinbe was the captain of the Sun pirates and a former Warlord, and he befriended Luffy while they were both in the underwater prison known as Impel Down. Luffy was there to save his brother Ace, and the two escaped with other inmates to go to Marineford to stop Ace's execution.
During the Summit War, Jinbe renounced his Warlord title and joined The Whitebeard Pirates, but when Whitebeard died he aligned himself with Big Mom, who agreed to protect Fish-man Island. After the Straw Hats stopped an attempted coup on the island, Luffy invited him to join the crew, and Jinbe agreed to join after severing ties with Big Mom, which happened after the Whole Cake Island Arc.