As the founder and captain of the Straw Hat Pirates, he is the first member that makes up the crew as well as one of its top three fighters. Luffy was one of eleven rookie pirates who had been referred to as "Eleven Supernovas", the eleven pirates with bounties over 100,000,000 to have reached the Red Line. Luffy's current bounty is 400,000,000, stated by the "impostor Luffy" after the time skip, and confirmed by one of the readings from a Pacifista.
He has a worldwide reputation for causing trouble, even among the Shichibukai, and the Marines, committing actions that were deemed dangerous by the World Government. Luffy has repeatedly committed crimes against the World Government.
He has gained a reputation for being 'reckless' and, in some cases, 'insane', after causing an incident in Enies Lobby, entering and escaping Impel Down, and joining the Battle of Marineford. He is therefore famous for being the only pirate to not only break into the 3 most important government facilities, but also for being the only one to escape all of them alive.
This, plus the fact that he punched out a Tenryubito with full knowledge of the consequences and his heritage has caused Luffy to be labeled as a "dangerous future element". He has eaten the Gomu Gomu no Mi.
Luffy, for the most part, has the same outfit throughout most of the series, as opposed to the rest of the crew, who change frequently. Luffy may wear a different outfit to suit the climate of an island (like a hooded parka on Drum Island or desert robes in Alabasta), but will switch back to his trademark vest and shorts after the adventures on that island are over.
Though Luffy prominently wears a red vest and blue shorts, he will wear his usual outfit in different colors. For example, in Enies Lobby he wore black shorts because they had pockets in which he could carry meat, on Thriller Bark he wore an orange vest and red shorts, and on Sabaody Archipelago he wore a blue vest and dark blue shorts. During the break-in at Impel Down Luffy was shown wearing a light blue vest with red shorts and after the fight between Magellan and Luffy, Inazuma gave him a yellow vest. He does, however, no matter where he is, wear his Straw Hat through absolutely everything, though at the start, the hat was prone to getting knocked off his head easily, forcing Luffy to either put it aside or have someone hold onto it during fights. He has since gotten a string strap for it which was sewed on by Nami, allowing the hat to hang from his neck during fights.
Luffy has been known to sport other miscellaneous items on his person from time to time. During the Skypeia Arc, he was seen wearing a black wristband around his left wrist with a white bangle over it, and after the battle against Moria in Thriller Bark, Luffy wore a decorated dark armband around his left bicep. This armband was later revealed to be a map that leads to Captain John's lost treasure, which Buggy sought for some time - leading to Luffy handing the armband in for Buggy in exchange for his services at helping him navigate through Impel Down.
During his return to Marineford to give a silent prayer, Luffy was briefly shown with four characters written on his right arm spelling
After those two years, Luffy wears a long-sleeved red cardigan with a yellow sash tied around his waist, somewhat reminiscent of Gol D. Roger's outfit. He does seem to have gotten only slightly taller and his hair is also slightly longer.
Luffy's current wanted poster.
Luffy in his youth.
Afro Luffy as seen during the Captain's Fight with Foxy in the Davy Back Fight.
Luffy's outfit at Thriller Bark.
One of Luffy's looks in One Piece Film: Strong World.
Luffy's outfit at Sabaody Archipelago.
Luffy as he appeared in the battle of Marineford.
Luffy after the time skip.
Luffy in his One Piece: Unlimited Adventure outfit.
Luffy in his One Piece: Unlimited Cruise outfit.