Harry Potter is a series of seven epic fantasy novels written by British author J.K. Rowling, portraying the adventures of Harry Potter and his companions as they study at Hogwarts School of Witchcraft and Wizardry, and their struggle against the evil Lord Voldemort. The series has since developed into a worldwide booming franchise, containing theme rides and movies. Harry Potter isn't mentioned or referenced as much in the show as other franchises, but Sheldon and Penny have both read the books, and Leonard had already read the first five by "The Spoiler Alert Segmentation".
In "The Cornhusker Vortex" (S03E06), Leonard tried to learn football by reading “Football for Dummies" book and watching it on television. Raj is not impressed by the commercials. Howard shows up and Raj is still mad at him. Leonard kept wondering about the stats of the game, such as a sack. Sheldon started describing all Leonard needs to know since his father made him watch football. Howard was astonished that Sheldon knew about football even asking "I mean, Quidditch, sure, but football ...?"
In "The Robotic Manipulation" (S04E01), Amy, Penny and Sheldon were talking about their lives. Sheldon says to Penny "I'm sorry, how is this better than uncomfortable silence?" Penny replies to Sheldon by saying "I don't know. I was just trying something." Sheldon was facing Amy and said "Muggles." He was presumably calling Penny a muggle.
In "The Toast Derivation" (S04E17), Sheldon was in Raj's apartment, watching TV with Howard. Sheldon and Howard were watching Harry Potter and the Sorcerer's Stone. Sheldon says "Oh, look, it's Harry Potter and 98% of The Sorcerer's Stone."
In "The Prestidigitation Approximation" (S04E18), Howard was showing Sheldon some card and magic tricks. Sheldon was annoying Howard, so Howard said to Sheldon "I'm saying believe in magic, you muggle."
In "The Shiny Trinket Maneuver" (S05E12), while Howard was practicing for his cousin's birthday party and did the trick with the cylinder and brought out a goldfish, Raj says that there's definitely a seat on the Hogwarts Express with Howard's name on it.
In "The Rothman Disintegration" (S05E17), Raj buys a Harry Potter Wand. Raj says "Would you look at this? I paid twenty five dollars to some kid on eBay for a handcrafted Harry Potter wand. He sent me a stick. He went into his backyard, he picked up a stick." Howard replied by saying "It's numbered." Raj replied by saying "Ooh, limited edition. Nice."
In "The Spoiler Alert Segmentation" (S06E15), Leonard was reading Harry Potter and the Half Blood Prince when Sheldon spoils the ending by revealing that Dumbledore dies, igniting an argument between the two. As Leonard storms out, Sheldon also spoils Book 7 by revealing the death of Dobby the Elf to spite Leonard. Later in the episode, Penny accidentally spoils that Harry Potter and Ginny Weasley become a couple to Leonard, much to his chagrin.
In "The Contractual Obligation Implementation" (S06E18), Sheldon says "I suppose there is a history of professional women using their initials so as not to be pre-judged. Harry Potter's J.K. Rowling."
In "The Table Polarization" (S07E16), Howard shows Raj a magic wand that acts like a TV remote. The wand is shaped like a wand from Harry Potter. Raj thought it was cool and said that "This is so much better than watching TV like a muggle."
In "The First Pitch Insufficiency" (S08E03), when Penny suggested Howard was the athlete among the guys since he was picked to throw out the first pitch at a baseball game, Sheldon reveals that all the guys are members of the third place Griffith Park Quidditch team (Raj- Seeker, Leonard- Beater, Howard- Chaser, Sheldon- Water boy), a game based off the sport from the Harry Potter books. "I know, watching your boyfriend run around with a broomstick between his legs isn't something you forget," quipped Penny.
In "The Positive Negative Reaction" (S9E16), Penny draws a Harry Potter face on Sheldon's face along with a moustache, a beard and two lines, one going between his eyebrows and one down his nose.
In "The Big Bear Precipitation" (S9E20), when preparing for their wilderness trip, Penny enters to tell Leonard that Amy is downstairs and finds Leonard wearing a backwards baseball cap. Penny wants to know which team it was for and it turns out to be the Hufflepuff from "Harry Potter".
In "The Birthday Synchronicity" (S10E11), when Sheldon and Amy were preparing to have sex, Amy brought two Harry Potter robes from the Universal Hollywood theme park enraging Sheldon since he wanted to go. After Howard and Bernadette's daughter was born, Amy took him to the park and then they returned for their sex routine.