Cosmologist Stephen Hawking made a short guest appearance in the fifth-season episode; in the eighth season, Hawking video conferences with Sheldon and Leonard, and makes another appearance in the 200th episode. In the fifth and sixth seasons, NASA astronaut Michael J. Massimino played himself multiple times in the role of Howard's fellow astronaut. Bill Nye appeared in the seventh and twelfth seasons.
The Canadian alternative rock band Barenaked Ladies wrote and recorded the show's theme song, which describes the history and formation of the universe and the Earth. Co-lead singer Ed Robertson was asked by Lorre and Prady to write a theme song for the show after the producers attended one of the band's concerts in Los Angeles. By coincidence, Robertson had recently read Simon Singh's book Big Bang, and at the concert improvised a freestyle rap about the origins of the universe. Lorre and Prady phoned him shortly thereafter and asked him to write the theme song. Having been asked to write songs for other films and shows, but ending up being rejected because producers favored songs by other artists, Robertson agreed to write the theme only after learning that Lorre and Prady had not asked anyone else.
Penny runs into her ex-boyfriend Zack, who has gotten rich from selling his company and married a similarly dim-witted woman named Marissa. Meeting with Leonard and Penny, they say Zack is infertile and ask to pay Leonard as a sperm donor so they can have a baby. Leonard is flattered, but Penny finds it creepy. Leonard says that since Penny decided she did not want to have children, he should be allowed to help another couple with this issue. Sheldon advises him to think about the emotional toll this could have on him. Leonard says he will not do it if Penny objects; Penny says she will support whatever decision Leonard makes. Meanwhile, Raj tries to get Anu back but she points out he just wanted to be married like his friends. Raj points out that Anu is similarly looking for a quick marriage. He admits to Anu that he really likes her and they decide to start their relationship as just dating.
When Bernadette tells Howard that she is expecting again, he is once again floored with fear about raising another child, particularly when he learns it’s a boy. Howard, who isn't athletically inclined, worries he will not be able to relate to a son who might one day expect his dad to be the stereotypical father. Despite his best attempts to get out of it, Howard has a vasectomy to avoid any future surprises and is placed on bed rest, joining his pregnant wife at home.
Science has also interfered with the characters' romantic lives. Leslie breaks up with Leonard when he sides with Sheldon in his support for string theory rather than loop quantum gravity. When Leonard joins Sheldon, Raj, and Howard on a three-month Arctic research trip, it separates Leonard and Penny at a time when their relationship is budding. When Bernadette takes an interest in Leonard's work, it makes both Penny and Howard envious and results in Howard confronting Leonard, and Penny asking Sheldon to teach her physics. Sheldon and Amy also briefly end their relationship after an argument over which of their fields is superior.
I read through the article and all the comments (which makes me miss TBBT even more and it hasn’t been off the air a week yet) and noticed that 3 of my favs aren’t mentioned. (1) episode where a bully (Todd Sornecki) steals Sheldon’s online trophies and Penny kicks him in the nuts for Sheldon; (2) the episode where they reveals each others secrets (Leonard slept with Priya; Raj used Sheldon’s tooth brush; Howard told Raj foreigner give gifts to Americans for certain holidays and Sheldon put moths in Leonards food “for science”; (3) the episode where Amy and Sheldon go to the aquarium “as friends”, when Sheldon tells Amy “I can handle a lot of things Amy but getting over you isn’t one of them, I think we should just be friends” it breaks my heart everytime; (4) the episode where Priya buys Leonard glass and he walks into the cafeteria and causes mass chaos, that’s a classic; (5) the episode where Priya ruins the roommate agreement between Sheldon and Leonard, when Leonard buys Sheldon Greek food it’s hilarious. Sheldon gets back at Leonard & Priya by threatening to send an email to Priya’s parents telling that “she’s in a relationship with the whiter than marsmellow fluff Leonard Hofstedter”. Ok just one more, when they all take a road trip to speak at the science convention and Bernadette runs into her former professor/lover played by Rick Foxx and Sheldon banished Penny to the “love car” and Bernie and Howard sing Sonny & Cher “I got you Babe” is funnier than hell. I still crack up when I see Raj look down at Howard’s junk to measure Howard’s junk against Rick Foxx’s, I can’t believe the sensors let that through.
However, no legal action was required to end production of the other show: as soon as it became known that the show was unlicensed, the actors quit and the producers canceled it. Dmitriy Tankovich (who plays Leonard's counterpart, "Seva") said in an interview, "I'm upset. At first, the actors were told all legal issues were resolved. We didn't know it wasn't the case, so when the creators of The Big Bang Theory started talking about the show, I was embarrassed. I can't understand why our people first do, and then think. I consider this to be the rock bottom of my career. And I don't want to take part in a stolen show".
Wil Wheaton brings William Shatner on his Professor Proton show to meet Sheldon, who gets so excited that he vomits on Shatner. Going to Wil to apologize, he finds Wil hosts a Dungeons & Dragons group with his celebrity friends including Shatner. Finding out Stuart is in the group and never told them, the guys make Stuart panic and quit. Wil secretly invites Leonard who discovers that the group also includes Shatner, Kevin Smith, Joe Manganiello and Kareem Abdul-Jabbar. Leonard tells Penny, who tells Amy and Bernadette, all three women having a crush on Manganiello. Because of that indiscretion, Wil kicks out Leonard and admonishes the guys for using him for his connections, and says that one of the worst things about being a celebrity is not knowing whether someone will like him for himself. To apologize, the guys invite Wil to play D&D with them at Leonard’s apartment, but Wil, secretly in the middle of a game with Penny, Amy and Bernadette and the group, politely turns them down, before allowing the girls to send them a photo of the events as payback.
Jim Parsons as Sheldon Cooper: Originally from Galveston, Texas, Sheldon was a child prodigy with an eidetic memory who began college at the age of eleven, and earned a PhD at age sixteen. He is a theoretical physicist researching quantum mechanics and string theory, and despite his IQ of 187, he finds many routine aspects of social situations difficult to grasp. He is determined to have his own way, continually boasts of his intelligence, and has an extremely ritualized way of living. Despite these quirks, he begins a relationship with Amy Farrah Fowler, and they eventually marry.
Amy and Howard begin collaborating on a neuroprosthetics project, upsetting Sheldon and Raj, who feel they are not spending as much time with them. When they seek solace with an annoyed Bernadette, she exploits the situation to trick Sheldon into doing Howard's chores. Penny successfully employs the approaches recommended in one of Bernadette's parenting books to deal with Sheldon, but Leonard believes she is coddling Sheldon too much. Sheldon and Raj resolve the issue of missing their significant others by spending time together.