The Weasley family has long accepted Harry as one of their own. Harry first interacted with them on his first day of school when he couldn't find Platform Nine and Three-Quarters. Ron and Ginny can be found on their own pages.
Harry first met Arthur after being rescued from the Dursleys by Ron, Fred and George. For as long as they've know each other, Arthur has asked Harry endless questions about Muggles, and Harry has, on more that one occasion, helped Arthur interact with Muggles and their technology. Arthur was more willing then Molly to tell Harry more of what was going on concerning the escape of Sirius Black. In Harry's fifth year, he witnessed an attack by Nagini on Arthur within the Ministry of Magic. Although Harry felt he had somehow been responsible for the attack, the truth was that he saved Arthur's life. Arthur survived the final battle.
Molly, the matriarch of the family, helped Harry find his way on his first day of school. She thinks of him as a part of the family. Throughout his Hogwarts years, she always sent gifts to Harry, including the famous Weasley jumpers/sweaters for Christmas. Before the final event of the Triwizard Tournament, Molly and Bill came with the rest of the champion's families to show support. Just before Harry's fifth year at Hogwarts began, she argued with Sirius about what Harry should know about the ongoing efforts of the Order. Some days after that, Molly took on a Boggart by herself, but was so overcome by what it showed her that she could not finish it. Harry witnessed the Boggart show each Weasley dead, one by one, and finally showing himself dead. During the battle of Hogwarts, Molly killed Bellatrix Lestrange, which caused great anguish to Voldemort.
Harry first heard about Bill during his very first trip on the Hogwarts Express. He did not meet him until the summer before his fourth year when Harry attended the World Cup with the whole Weasley family. Bill did come along with his mother to wish Harry well on the last Triwizard task. After Voldemort's restoration, Bill moved back to England in order to work with the Order of the Phoenix. The trio stayed an extended period of time with Bill and his wife, Fleur Delacour (the Beauxbaton's Triwizard champion), at their house after their escape from Malfoy Manor. Both Bill and Fleur survived the final battle.
Charlie was of immense help to the trio and Hagrid in Harry's first year. His fellow dragon caretakers took Norberta (known as Nobert at the time), a baby dragon, back to Romania where he worked with dragons. Charlie also joined the Order of the Phoenix, but remained in Romania. Like the rest of his family, he joined in the final battle.
Harry and Percy never really got along because he had a bit of a pompous attitude that only grew as time went on. Percy began to work for the Ministry after his graduation from Hogwarts. His beliefs even began to mirror the views of many in the Ministry, especially when it came to Harry. In Harry and Ron's fifth year, Percy sent a letter to Ron warning him to stay away from Harry. Percy eventually cut off all ties with his own family. However, he returned to Hogwarts and joined his family for the last confrontation.
Fred and George
Harry first met Fred and George just before boarding the Hogwarts Express for the first time. The three of them were on the Gryffindor Quidditch team (the twins played as beaters) together. The twins gave Harry the Marauder's Map (which had actually been created by James Potter and his three best friends) during his third year. This allowed Harry to finally go to Hogsmeade undetected and would play a significant role in many adventures. Harry later returned the favor by giving the twins his entire winnings from the Triwizard Tournament. With the extra money, they were able to start their own joke shop (Weasleys' Wizard Wheezes). The twins were among those who helped get Harry out of Little Whinging. George lost an ear in the ensuing battle with the Death Eaters. The twins, along with some Order members, participated in a secret and illegal radio broadcast during the following year. It was meant to keep people informed on the activities of the Death Eaters. Along with their siblings and parents, the twins participated in the last battle. Fred was killed not long after the battle started which devasted Harry.