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 argubly 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 physicis.
The Large Hadron Collision, where Sheldon tries to convince Penny that he should accompnay 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 extrordinary 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 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 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.
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 unsucessful, they feel more affection to each other and feel closer.
Amy herself proposed the alternate reality where an unattached Penny would go after Sheldon. In "The Cooper Extraction", 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 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.