Season 1 and 2 of The Big Bang Theory produced some of the most hilarious episodes of the entire series, but it wasn't until season 3 where the show truly hit its stride.
It would still take another year for the show to get its first Emmy nomination for Best Comedy, but Jim Parsons had already been nominated for Best Actor in a comedy for season 2 and would end up taking home the hardware for TBBT's third go-around. Pair that with Leonard and Penny finally getting together and you get a forever-fan-favorite season.
The Electric Can Opener Fluctuation, Episode 1 (8.4)
The very first episode of the season had the boys return from their arctic expedition to the North Pole. Penny kisses Leonard as soon as she opens her door and they start their relationship while Howard and Raj admit to Sheldon that they tampered with his experiment due to his terrible demeanor and attitude. Sheldon can't accept the betrayal and resigns from his job and flies home to Texas. When the guys show up to bring him home and can't sway him, Sheldon's mother steps in and says a few words about evolution and the Bible - and Sheldon forgives his friends and goes home.
The Vengeance Formulation, Episode 9 (8.4)
One of the main reasons that season 3 is so prominent in the history of The Big Bang Theory is that it introduced two characters who would become series regulars for the rest of the show - Amy and Bernadette. In this episode, Howard reaches his third date with Bernadette and has to decide whether or not he wants to commit to her before they have sex. In his attempts to make a choice, Howard comes to the conclusion that he should propose to Bernadette - she obviously denies him but a tribute song keeps them from breaking up. Meanwhile, a colleague/enemy of Sheldon plays a trick on him while he is being interviewed by NPR. Sheldon tries to concoct a prank to get his nemesis back - in typical sitcom fashion the prank backfires (but also in sitcom fashion nothing comes of it).
The Excelsior Acquisition, Episode 16 (8.4)
The Big Bang Theory became highly notorious for its sci-fi/comic book guest stars in later years, but during the first few seasons it was a genuine treat any time a nerdy celebrity showed up. During this episode, Sheldon must attend traffic court due to his running of a red light when Penny was injured and had to be taken to the hospital. Unfortunately, while in traffic court, Sheldon not only misses a comic-book signing at Stuart's store where Stan Lee is giving autographs but he also ends up getting tossed in jail. The episode ends with Penny trying to apologize by bringing Sheldon to Stan Lee's home (unannounced) and getting the cops called on them. Sheldon did get finally get an autograph - on a restraining order.
The Einstein Approximation, Episode 14 (8.5)
Sheldon never shied away from letting Penny know what he thought about her menial waitress job at the Cheescake Factory, but this episode took it to another level. When Sheldon reaches a "block" and can't make any ground on a problem he's trying to solve, he resorts to trying several different methods of study (all crazier than the next) in order to achieve his answer.
When he still can't, he decides that taking a job at the Cheesecake Factory as a waitress (Penny's job) is the most degrading job he can think of and will help him open up the inner mechanisms of his mind. His plan works, but it was still a super cheap-shot at waitresses.
The Precious Fragmentation, Episode 17 (8.5)
Lord of the Rings will forever be in the conversation for best sci-fi/fantasy franchises of all time so it was only natural that the group of nerds did an episode revolved around Middle Earth. The guys bring home a box of random film memorabilia that they picked up at a garage sale and find tons of hidden treasures - including a ring that turns out to be the actual ring from Peter Jackson's movies. The boys understandably fight over who owns it, finally deciding that the last person holding the ring gets to keep it.
The Pants Alternative, Episode 18 (8.5)
In this episode, Sheldon gets notified that he has won a prestigious award and has to make a speech during the ceremony otherwise he has to forfeit the victory. He then reveals to the group that he has stage fright and can't do it, prompting the group to do everything they can to calm his nerves. They all blatantly fail and Sheldon ends up having to get plastered in order to make it up on stage, resulting in one of the show's most comedic scenes where Sheldon loses his pants and mentions Uranus for good measure.
The Gorilla Experiment, Episode 10 (8.6)
Another episode that takes a cheap shot at Penny centers around Penny asking Sheldon for physics lessons so that she can talk to Leonard about his work. Sheldon puts Penny down for being stupid and finally has to result to making her memorize a condescending statement (which Penny doesn't realize) in order to play it off as if she learned anything. Meanwhile, Howard spends the episode jealous that Bernadette is interested in Leonard's laser experiment and goes crazy-boyfriend on him - it doesn't work.
The Lunar Excitation, Episode 23 (8.7)
Ladies and gentlemen, give a warm welcome to Amy Farrah Fowler! This is the episode that saw the introduction of the woman who would end up being Sheldon's soulmate was the season three finale and it changes The Big Bang Theory forever.
Thanks to Howard and Raj plugging Sheldon's personal information into a dating website for fun, it resulted in Amy and Sheldon matching and deciding to meet for a "date". Once they've met, it turns out that they're practically the same person and they decided to begin their friendship/relationship.
The Adhesive Duck Deficiency, Episode 8 (9.0)
This was the episode that was the result of Sheldon receiving his traffic-light ticket made necessary by Penny slipping in the shower, dislocating her shoulder, and needing to be driven to the hospital. Since everyone else is away on a camping/star-gazing trip, Sheldon is the only one who can sit behind the wheel and the result is as funny as expected. Mix that plot-line with the B-story of Leonard, Raj, and Howard getting mind-numbingly baked after they eat some cookies given to them by Grateful Dead fans and that makes for one laughter-filled episode.
The Staircase Implementation, Episode 22 (9.1)
Audiences had been watching The Big Bang Theory for nearly three whole seasons before the show decided to bless them with this particular episode - the origin of how Sheldon and Leonard became roommates. The episode flashes back to the day that Leonard and Sheldon meet and covers topics such as Leonard's roommate interview, the signing of the notorious roommate agreement, the creation of Sheldon's "spot", how the elevator ended up broken, and multiple others. That's a lot of backstory to fit into a 22 minute episode and not a single minute was wasted.