The murder victim in last night’s episode of Law and Order: Criminal Intent bore a strong resemblance to the Burt Lancaster character in Sweet Smell of Success. Mike Logan even mentioned it.
“Fame” did a musical adaptation of “Othello” (“Desde- Desde- DesdeMOna!”) and also a version of “The Wizard of Oz.” The former was IIRC presented as a stage show within the episode so may not count, but I’m pretty sure the latter included the tropes of the 1939 film, including being partially in black and white.
“Veronica Mars” is another that did a “12 Angry Men” episode, called “One Angry Veronica.”
One episode of Thirtysomething was definitely based on James Joyce’s wonderful “The Dead.” Surprisingly well done.
And a “holiday” episode of Xena was based on “A Christmas Carol.” With the help of her gang, Xena convinced a miserly old king not to foreclose on the orphanage during Equinox season.
Not quite what the OP was asking for, but another Simpsons episode centered on Marge’s role in a musical version of A Streetcar Named Desire. I laughed heartily at a premise I thought too funny to ever come true, only to be nonplussed by the appearances of Andre Previn’s opera version.
I must have missed that one, can I get a recap?
Tiny Toon Adventures did a great Sunset Boulevard parody. (“I am big, it’s the cartoons that got small!”)
In high school I had to write an essay on The Taming of the Shrew, and I wrote it based on that Moonlighting episode. I got an A! 
Speaking of Star Trek: wasn’t the episode (whose name escapes me) that involves the Enterprise dueling with an invisible (cloaking device) Klingon starship essentially a remake of a WWII submarine movie (possibly The Enemy Below)?
Ditto Remington Steele. (I remember seeing this as a kid, and saying, hey, waitaminnit, about halfway through.)
Now that you mention it, and I recall it, I believe you are most definitely correct.
Best Rashomon that I ever recall was an episode of Wings. Everyone of course was the hero in their telling, but when Antonio told his version, they showed it in black and white and treated it like an old Italian movie. Quite funny.
Does Sliding Doors count as an inspiration? Because there was Sliding Frasiers. That show also had a slightly Rashomon-esque episode too, once.
The John laRoquette Show did a wonderful take-off on Sunset Boulenard, with Betty White as the aging star who thinks she’ll get speciasl coverage in TV Guide (“I’m ready for my close-up…box!”)
It was called Here we Go Again:
Yet another is Dawson’s Creek episode “The Longest Day” (season 3, episode 20.)
My favorite It’s A Wonderful Life episode was done on a show I almost never watched: Popular. The OC’s version of it was decent too.
The Lost World did a great version of The Masque of the Red Death at one point as well. Their take involved the cast discovering the castle from the red death, being possessed by the evil people who were in the story, and reenacting the events.
From tv.com:
It was black and white; I vividly recall Brain wading through the brick-lined tunnels of Vienna.
The British sitcom Nightingales , from 1990 ish, did a riff on King Lear and another episode which was a bit of a mishmash of Shakespear plays. It was a while ago and my memory is fuzzy.
30 Rock’s “Amadeus”? With Tracy Jordan’s gift with porn?
Huh, CSI’s riff on that movie called it the exact same thing.
Doctor Who has done it a few times.
Planet Of Evil is a mixture of Forbidden Planet and Doctor Jekyll and Mr Hyde.
The Androids Of Tara is The Prisoner Of Zenda.
The next episode to be broadcast Turn Left is rumoured to be a version of Sliding Doors. (unconfimed)