I forgot to mention that during Dick’s take, the couple is not shown. You just see the open door at the edge of the scene, and Dick’s antics. It’s not until Greg Morris walks in that the audience knows what was going on.
And that was very daring for 1963… The words “colored” and “Negro” were not spoken. Here is wiki’s write up.
I’m another one who as soon as I saw the title I thought of this.
The one where the curtain rod is still on her shoulders?
I think eventually Harvey Korman mentions “Love your dress” and she replies “Oh, it’s just something I saw in the window…”.
Don’t know if it was wordless, but…
Tim Conway as the clumsy dentist
Harvey: Scarlett, what a lovely dress.
Carol: Thank you. I saw it in a window and just couldn’t resist.
Pick just about any episode of Mr. Bean and you can find a contender somewhere in it.
All the grunting and mumbling in the aforementioned Niles Crane scene made it hard for me not to think of Bean, too.
I’d nominate Frasier as the champion series for this category, though. It seems almost every episode had a silent scene behind the end credits, and they always seemed like gems to me.
Of the curtain+curtain rod dress, paraphrasing(kinda), “I saw it in the window and just had to have it!”
I actually thought of that scene, too, but it’s not wordless. Korman doesn’t speak, though, so maybe we can give it half-credit. God, it’s funny.
Not strictly a sitcom, but the entire “The Dull Life of a City Stockbroker” sketch from Monty Python is a classic.
The brief bit from The Drew Carey Show when he sits down wearing his new pleated pants and they fold to look like he has a boner knocked me right off the couch.
And the episode of The Odd Couple when Felix lost his voice, walked over to the blackboard, and wrote “HONK” was also great.
From the same episode, Xander “saves” Anya from Spike, and she shows her appreciation: http://www.youtube.com/watch?v=ZFfjsn4HRFs
*** Ponder
Steven Colbert’s Daily Word after the democrats took the house and senate in 2006 is classic.
The word was Sigh
http://www.colbertnation.com/the-colbert-report-videos/77985/november-08-2006/the-word—sigh
Four of the six I immediately thought of have already been mentioned:
Niles ironing his pants
Carol Burnett and the curtain rod
Archie & Sammy
Dick Van Dyke and the black couple
And the remaining two are:
Mary Tyler Moore at Chuckle the Clown’s funeral
Golden Girls’ Sophia and Dorothy as Sonny and Cher (not really wordless; they sing “I Got You, Babe”
Like the Buffy episode “Hush,” Two Guys and A Girl did a dialogue-less episode called “The One Without Dialogue.” It was pretty funny overall, but I liked Ashley being hounded by a group of pregnant women for not giving up her seat on the subway best.
all I can find are parts 2&3, sorry 
Is Red Dwarf technically a sitcom?
Anyway, Terrorform.
http://www.youtube.com/watch?v=OMMoO7GV9hU
Lister goes silent about 3:11 and Cat about 3:47. I’ve seen this scene too many times to count and I still crack up every time.
My appreciation for you will never dim, Zip.
Not silent. She is trying not to laugh during the minister’s eulogy.
There was a great scene in Three’s Company where Jack Tripper, dressed in a tux at a formal party, did this amazing dance sequence. There’s a little bit of it in this clip but the whole thing is astonishingly funny, particularly since John Ritter was not a dancer.
I liked Les Nessman’s appearance disguised as a black man, with a 1970’s Afro, on WKRP in Cincinnati.
Almost all of the scenes mentioned are not wordless. They are dialog scenes with a sight gag. The OP asked for scenes with “no dialog”.