The scientific overachievers of kinds of amazing games throughout the show's run, and they were dead-serious about it. The game sessions played a remarkable role in the show: They not only had fun together but also escaped reality and killed some time together as they bonded through fiction.
Whether it's a weekend-long marathon or a relatively extended car ride, the gang enjoyed multiple genres of games throughout the years, and board games weren't an exception. From old-school role-playing games like D&D to head-scratching 3D chess sessions, fans loved seeing the gang play these tabletop games in the show.
Jenga
In "The Fuzzy Boots Corollary" (season 1, episode 3), Howard, Raj, and Sheldon are in the middle of a philosophical discussion at their usual spot around the table while playing Jenga. Howard asks Sheldon if he would like to know if he was a robot, and Sheldon throws a counter-question: "When I learn that I'm a robot, would I be bound by Asimov's three laws of robotics?", referencing Isaac Asimov's "The Three Laws," the fictional ethics system he created.
This scene marks a symbolic moment of their intellect and relationship dynamics through Jenga, unlike another time the game appeared in the show as a giant version in the twelfth episode of the sixth season, where Sheldon channeled his inner child and had a great time. The game was also briefly mentioned in "The Zazzy Substitution" in Sheldon's sarcastic comment and actually played in "The Wildebeest Implementation" as the Donkey Kong version.
Dungeons & Dragons
Since the guys were very ionate about storytelling and roleplaying, it wasn't really a surprise that the game, Dungeons & Dragons, appeared in multiple TBBT episodes (either dominating a whole sequence or being mentioned in-jokes and references).
However, as the years went on, it seemed to become a group activity that all characters enjoyed as it brought them all closer together and revealed new sides that people had never seen before. Among many D&D inclusive episodes like "The Wiggly Finger Catalyst" (season 5, episode 4), "The Love Spell Potential" (season 6, episode 23), or "The D&D Vortex" (season 12, episode 16).
Star Trek Tri-Dimensional Chess
The chess variant, as seen in the original and subsequent Sheldon enjoying every second of it as an intelligent scientist and a die-hard Star Trek geek.
However, as time marched on, the game ended up playing a significant part in Sheldon's character development, where the game went on to serve as a symbol for Sheldon's loyalty towards Leonard (as seen in the season 7 episode, "The Hofstadter Insufficiency"). It surely caused many "aww"s when Sheldon set up the board, trying not to it the truth that he was trying to bond with Penny over missing Leonard because he would exclusively play this game with him.
Pictionary
In "The Re-Entry Minimization" (season 6, episode 4), Penny, Sheldon, Amy, and Leonard team up as boys vs. girls for a Pictionary night, before Howard's homecoming from space. They rapidly realize that Sheldon's genius seems a bit too much for graphic practicality in the funniest way possible.
Pictionary worked as a catalyst in this sequence: As Penny proves herself as the smartest one in the room for a change, she shows that street smart sometimes beats book smart. Also, the way Sheldon confuses "polish" and Polish," pouring too much of his knowledge into a pretty simple game, is still too hilarious to watch without a giggle.
Talisman
Considered one of the best fantasy adventure board games of all time, Talisman appeared several times in The Big Bang Theory, as some dedicated fans may have already noticed.
The fantasy-themed quest game accompanied the boys of TBBT while some drama going on, like in the episodes "The Peanut Reaction" and "The Tangerine Factor" of the first season, and also served as a time-killer in "The Financial Permeability" and "The Spaghetti Catalyst." Sadly, it didn't get as much attention as all the other games but avid fans may also notice that the boys have the 4th edition of the game.
Forbidden Island and Ticket to Ride
In "The Anxiety Optimization" (season 8, episode 13), the visually rich and cooperative game Forbidden Island and the railway-themed euro-style game Ticket to Ride are seen at the same time.
As some fans may agree, it would have been interesting to actually see them playing both games since they're not as popular as the other ones. Although not being played, both games served as a nice touch to the sequence to gain viewers' hearts who paid attention to details, while increasing the dose of geekiness in the show if it's possible.
The Settlers of Catan
Another less-popular multiplayer board game, created in 1995, The Settlers of Catan appeared in The Big Bang Theory as a notable touch to the geekiness level of the show. In it, each player embraces their roles as "settlers" and tries to grow their holdings via exchanging and acquiring resources while getting rewarded with points when their settlements expand.
In "The Recombination Hypothesis" (Season 5 Episode 13), The Settlers of Catan briefly served in word-based humor. When Sheldon insisted on saying "wood" and stayed oblivious to what it might reference other than a material he needs to build a road in the game. Raj and Howard cracked up for a good while, and the viewers are still probably quick to them.