I’m compiling a list.
Off the top of my head:
Buffy’s “Once More, With Feeling” (IMHO, the standard against which all others are measured and inevitably fall short)
Scrubs’ “My Musical”
…and wasn’t there a Moonlighting episode with a convict gang that broke into song?
What else? (The top of my head didn’t get too far).
Simpsons did a few, I think. Definitely Simpsoncalifragil…doh…cious. Maybe a clip show as well.
And I guess if we want to just shut the thread down, there’s always TvTropes: http://tvtropes.org/pmwiki/pmwiki.php/Main/MusicalEpisode
Drew Carey Show had one each season.
The Dick van Dyke Show didn’t have musical episodes, but put musical numbers into quite a few.
That’s awesome. Thanks.
Seems like most shows that have a good singer/broadway performer will eventually find an excuse to get them to sing.
How I Met Your Mother, the big musical number: How I Met Your Mother Season 05 Episode 12 Girls Versus Suits Suits Song - YouTube
I begged my (female) college roommate to watch an episode of Xena with me. It ended up being the musical one, she looked over and said “Are they all like this?”
The whole episode, or is one musical number sufficient?
There was an episode of Two and a Half Men that broke out into a Broadway-style show tune.
In one *Taxi *episode, the cast danced to Lullaby of Broadway.
In The Big Bang Theory, Raj and Bernadette once performed a Bollywood-style routine.
Daria did one.
Ally McBeal
Pushing Daisies had Kristen Chenoweth singing “Hopelessly Devoted to You,” plus had her do a duet with Ellen Green for “Birdhouse in Your Soul.” I’m disappointed that, with great Broadway singers like that, they didn’t do it more often.
One episode of Mad Men was not a musical but did include several performances.
The copywriters, stuck in the office over the weekend, resort to marijuana. The dealer went to Princeton with one of them–we hear an a capella performance as they reminisce about the old college days.
Roger hosts a party that includes his cringe-inducing blackface performance. And a snappy Charleston danced by Pete & his wife.
Finally, Joan’s horrid husband tries to embarrass her by making her play accordion for dinner guests. She sings “C’est Magnifique” charmingly…
Pushing Daisies had Kristen Chenoweth singing quite a bit IIRC.
Phineas and Ferb - Rollercoaster The Musical! (even more musical than their regular shows). 
“The Nightman Cometh” episode of It’s Always Sunny In Philadelphia (which was also performed live)
Gilligan’s Island, “The Producer”
I ask to be, or not to be
That is the question that I ask of me…
Not to mention the episode with the Mosquitoes (Bingo, Bango, Bongo and Irving).
Towards the end of the second season of American Horror Story, there’s a big musical number in the creepy mental asylum.
The fact that it’s in a mental asylum should give you some idea about what’s really happening during the scene.
Grey’s Anatomy did a musical episode.
I thought it was kind of weird.
Lest we forget:
The musical version of The Honeymooners and some other experiments in combining continuing storylines and characters with musical numbers.
Why wouldn’t you?