To the list of must-watch episodes, I would add these (all but the last are available on Netflix Streaming, and the last one should be on CBS.com for a while):
“Drumroll, Please”Season 1, #13 Ted recounts an amazing date at a wedding. This is one of the show’s earliest wins in storytelling with multiple layers of flashbacks and multiple points of view.
“The Scorpion and The Toad”&“Bachelor Party”Season 2, #2 & #19 These are definitely a pair. In the first episode, Barney takes Marshall on a series of increasingly terrible nights of bar-hopping. Barney’s reasons become clear 17 episodes later.
“Single Stamina”Season 2 #10 One of the show’s rare successful attempts to create a new catch phrase; also, it’s real. [Falls asleep]
“Stuff”Season 2 #16 For Barney’s play alone, you should watch this.
“No Tomorrow”Season 3 #12 This episode touches on a lot of the show’s best themes: The battle of Good-natured Ted vs. Douchbag Ted, and Ted and Marshall’s complicated friendship.
“The Chain of Screaming”Season 3 #15 Another of the show’s best themes is that you don’t always get what you want, and that’s OK.
“Sandcastles in the Sand”Season 3 #16 I love any Robin episode, and this one in particular introduces us to her long-lost boyfriend (James Van Der Beek) and “Murder Train”.
“The Naked Man”Season 4 #9 This is a purely silly episode where the gang learns of a new way to woo the opposite sex.
“Three Days of Snow”Season 4 #13 This is another classic episode that plays with time and flashbacks to a glorious conclusion.
“Duel Citizenship”Season 5 #5 For the Kenny Rogers audiobook and TANTRUM!
“Symphony of Illumination”Season 7 #11 Robin loses something that she thought she didn’t want anyway. Totally heartbreaking.