There is an astonishingly funny scene around the mid-end of the second season where Gordon Cole (played by David Lynch) tries to flirt with Shelly Johnson. The running-joke of Cole's hearing problems is made fresh and funny, and adding the Log Lady into the mix just made it even more amazing.
And adding onto that, Bobby's expression when he walks in and sees Cole and Shelly kissing is something that must be seen to be believed.
In one scene in the second season, Windom Earle is listening to the police discussing his schemes via a Tracking Device in their office when Cole suddenly notices the bonsai tree where the device is hidden and leans over it:
Cole: REMEMBER THOSE OLD WORLD WAR II MOVIES? BONSAI!!!
Earle:(clapping a hand to his ear) Agh! Damnation!
The scenes where Ben Horne looks back on his childhood.
The drunk Icelandic delegation on Cooper's inn floor.
Pretty much any of the guests in the background at the hotel. They range from cheerleaders, to marching bands, to a barbershop quartet, and many more. They're never explained, never even really acknowledged, they're just...there. It just seems to bizarre to have a fairly quiet scene of Dale and Albert talking over coffee, when there's a barbershop quartet humming to themselves in he background!
Cooper and the llama.
Ben's mental breakdown and re-enactment of the Civil War in the second season.
Later in season 2, when the pageant judges are discussing what they want in a Miss Twin Peaks, a very exasperated extra walks in front of them carrying a stuffed deer. It looks like he's having sex with it!
The scene where Garland Briggs slaps a cigarette of Bobby's mouth, causing it to land in Mrs. Briggs's meatloaf.
Cooper's deductive technique involving the throwing of rocks at a glass bottle.
Audrey's successful attempt to wreck her father's impending deal with the Norwegians, by informing them of Laura Palmer's murder.
Hawk: One woman can make you fly like an eagle, another can give you the strength of a lion, but only one in the cycle of life can fill your heart with wonder and the wisdom that you have known a singular joy. *Beat* I wrote that for my girlfriend.
"I've got good news. That gum you like is going to come back in style."