The main reason for the interest in Sheldon and Penny is the chemistry between them and the comedic interaction this creates. The fans like to think of a world where they might develop a relationship, despite the direction the show has chosen to pursue.The interaction between Sheldon and Penny has been praised by critics. James Chamberlain of IGN wrote: "Cuoco and Parsons are great in their own right, but when put together, they truly shine." Matt Roush of TV Guide said that Sheldon and Penny's "scenes and episodes together are usually Big Bang at its best." Todd WanDerVerff of The A.V. Club wrote that they "made such an inspired odd coupling that at times, it seemed as though the entire show were about them" and their chemistry "has some of the rattle and rhythm of the great comedic duos".
The Shenny fandom was at its strongest during Season 1-4. The group became so large that fans set-up their own forum on Livejournal's Paradox. Founded on 23 July 2008, Paradox members followed the show for a number of years. Later, a website dedicated to Sheldon and Penny was founded called www.thebigbangtheoryhq.com.
The most notable Sheldon and Penny episodes appear in the earlier seasons. Sheldon analytical mind versus Penny's down-to-earth heart, clashed wonderfully from the very start. Much loved Sheldon and Penny episodes include:
Season one's The Pancake Batter Anomaly features Penny playing nursemaid to Sheldon when he gets sick. Exposing for the first time, how a biological frailty as simple as the common cold, renders Sheldon beyond useless. His lack of awareness is at its peak and Penny's reluctant compulsion to help, coupled with the increasing intimacy of his requests, is what makes this a Shenny favorite. It's also the first time we hear them sing Soft Kitty.
In "The Barbarian Sublimation:" , Penny becomes addicted to Age of Conan online game and Sheldon becomes her mentor. Howard and Raj remark on the strangest of this union. "Like if Hulk were dating Peppermint Patty." One of the few episodes that is about Penny herself and not simply a romantic interest.
The Panty Piñata Polarization shows these two are evenly matched and also incredibly funny. Penny refuses to back down when Sheldon imposes a ban from their apartment.
The Bath Item Gift Hypothesis is arguably one of Big Bang's most famous moments. Sheldon delivers his first show of real human intimacy when his plan to match her Christmas gift giving fails when Penny gives him a present which emotionally floors him.
The Adhesive Duck Deficiency was the episode which really rocked the boat and brought the Shenny fandom to life. Sheldon is forced to help Penny get to hospital after she dislocates her shoulder in the shower. After this episode, aired the media picked up on the Shenny buzz and the fandom exploded. Later that season Sheldon was introduced to his now girlfriend Amy leading to much speculation about the timing within the Shenny community.
Other early season favorites:
The Financial Permeability, where Sheldon gives Penny money to pay her rent.
The Terminator Decoupling, where Sheldon leaves his flashdrive at home and has to call Penny for assistance. She discovers letters from his Meemaw and his pet name, Moonpie.
The Work Song Nanocluster, where Sheldon helps Penny set up a business selling Penny Blossoms.
The Vegas Renormalization, where Sheldon sleeps in Penny's bed after he gets locked out of his apartment.
The Gorilla Experiment, when Sheldon teached Penny some physics.
The Large Hadron Collision, where Sheldon tries to convince Penny that he should accompany Leonard to see the CERN, and he hugs her.
The Pants Alternative, Penny takes Sheldon shopping for a new suit.
The Spaghetti Catalyst. They have dinner after the break-up and Sheldon goes to extraordinary means to keep the date, and hide it from Leonard.
Later episodes have a different dynamic, focusing more on a bond between them rather than the opposites trope, like the following.
In the context of the series, they have been said to have a relationship who's closeness even bothers Amy per "The Viewing Party Combustion". When Leonard and Penny are fighting Leonard mentions the weird relationship she has with Sheldon which she denies. But the Shenny relationship for fans of a romantic bond is purely hypothetical and doesn't necessarily rely on canon, even though they are portrayed almost like brother and sister.
"The Infestation Hypothesis" we see Sheldon spending his time in a new chair, which Penny brought into her apartment. Reading together, Penny regarded them as an old married couple.
After more or less absent in the previous seasons, the seventh season picked up on the pairing once again:
In "The Hofstadter Insufficiency", Sheldon and Penny spend their days together, while waiting for Leonard to return from the Hawking expedition.
In "The Scavenger Vortex", Sheldon and Penny join forces on a scavenger hunt quest. This episode particularly highlights how Penny's street smarts and knowledge of pop culture complement Sheldon's extraordinary analytical skills. Together, they make up a very capable team.
In "The Cooper Extraction", Amy herself proposed the alternate reality where an unattached Penny would go after Sheldon. Shenny has a fantasy sequence about an alternative reality where Penny attempts to seduce Sheldon in the Laundry room. However, this only exists in Amy's mind as she considers the "what ifs" possible if she and Sheldon had never met Leonard.
In "The Occupation Recalibration", Sheldon accompanies Penny, when she decides to quit her job as a waitress and focus on acting. Unlike Leonard, Sheldon supports and encourages her decision, leading to the line: "The best way to achieve a goal is to devote 100% of your time and energy to it."
"Anything Can Happen Recurrence" Another episode, where Amy expresses her concern regarding the close relationship between Sheldon and Penny. After being lied to by their friends, Penny and Sheldon go out on a dinner to support each other, "because that's what friends do." Amy later confesses to Leonard about her jealousy for the close relationship and connection between Sheldon and Penny. She wishes Sheldon would be so comfortable around her already. At this point, Sheldon and Amy have been a couple for almost four years.
In "The Intimacy Acceleration", Penny and Sheldon conduct an experiment designed to make two people fall in love. The test is loosely based on a theory by psychologist Arthor Aron, called ‘The Experimental Generation of Interpersonal Closeness’ and although they decide the test was unsuccessful, they feel more affection to each other and feel closer.
In "The Separation Oscillation", Sheldon suggests that Penny kiss someone else since Leonard was unfaithful to Penny kissing the girl on the boat. Penny agrees and gets into a very passionate embrace with the newly single Sheldon. The whole scenario was a nightmare that Leonard had forcing him to fix the argument he had with his new wife.
In "The Hot Tub Contamination", after bickering with his live-in girlfriend Amy, Sheldon declares that he is looking for another woman. While searching for a new girl at an ice cream parlor, Sheldon remarks that he is sorry that he hurt Penny. He didn't ask her first as a replacement for Amy. Penny just stares at him.