Fran in The Nanny. Max and Niles hang a lampshade on this at one point when they debate what a certain word means, despite both being British.
In face, almost every member of the Fine family uses Yiddish words at one point, especially Sylvia and Yetta.
Non-Jewish characters also use Yiddish words and phrases, most notable Val, Grace, and occasionally Niles, though only for comedic effect.
Aaron Sorkin loves this one, especially when he can subvert it:
Lampshaded and subverted in Sports Night, when Isaac, an African-American (played by Robert Guillaume), busts out the phrase, "What, am I from Minsk-a-Pinsk?". When called on it, he claims that Yiddish phrases, "work for him." He is summarily informed, "Not as well as you think they do."
Most characters especially the New York-area Jews Toby and Josh, will successfully pepper their speeches with Yiddish... and Jed and Leo, probably thanks to a lifetime of politics, will have at least a passing familiarity. In "Enemies Foreign and Domestic", Jed comes out with a beautifully inflected Vas vilst du fun mein layben?
Subverted when Donna — a blonde Midwesterner — tells Toby that Josh is recovering from being shot, and he doesn't need Toby "going over there and getting him fuhtushed. Toby, a New York Jew, corrects her pronunciation of "fartoost" and tells her, "don't bring the Yiddish unless you know what you're doing."
Subverted when Toby goes into a monologue about how a particular night is special, CJ interrupts "We dip twice and eat gefilte fish?" He replies "Suzie Creamcheese, do not attempt the Haggaddah" and she responds "I know how to bless the soup, too."
Subverted somewhat in flashbacks about Toby's father, showing him fully conversant in Yiddish as a member of the Jewish Mafia.
Munch only occasionally used Yiddish on Homicide: Life on the Street, although he did once teach it to Kellerman for his own amusement. It did, however, come in handy after he switched over to Law & Order: SVU, when they suspected a Rabbi of sexual misconduct and he fled New York to a Jewish community upstate where even the cops were Jewish and decided to shelter him. When Munch and Stabler arrive their local police contact is told (In Yiddish) to keep them away from the synagogue, and Munch overhears and thus deduces where the Rabbi is being hidden.
As a New Jersey Jew, Jon Stewart frequently uses this trope on The Daily Show, but reprimanded Brian Williams for using one too many Yiddish words in an interview:
Stewart: What's with the Yiddish tonight? What's with the — "shmaltzy", and the "just gave me a little schpilkis, but" — "I took my punim over there", bing bang boom — Williams: Joey Bishop, ladies and gentlemen.
The correspondents, however, have been granted Y-word privileges, and Jewish stories often have John Oliver or Jessica Williams speaking Yiddish every third word while Jon Stewart corpses all over the anchor desk.
On an early Series 4 episode of Doctor Who, The Doctor tells Donna, "I'm tired of the shmoozing." Being The Doctor, of course, he can most likely speak Yiddish fluently just like practically every other human language.
Parodied in the episode of Frasier, "Merry Christmas Mrs. Moskowitz," where (as part of a Fawlty Towers Plot) Frasier needs Niles to pretend to be Jewish for reasons too complicated to explain. Niles takes the job to heart, liberally injecting common Yiddish words into the conversation.
In one episode, even London uses some Yiddish when she mentions she celebrates Hannukah (for the extra presents).
House is sporadically prone to this, originally when in context of referring to Jewish people but later on just to throw off his co-workers.
House also presents us with Cuddy's incredibly Jewish mother, who isn't even Jewish. (She converted, but seems to have gone whole-hog; it rather reminds one of a certain Walter Sobchak).
On Covert Affairs, Eyal distracts Annie while pickpocketing her by telling her she has some "schmutz on her collar".
Subverted in one episode of Northern Exposure, Joel Fleischman finds out that the local Indian tribe has adopted several Yiddish words and phrases into their native language, due to the influence of a 19th Century Jewish doctor who joined the tribe and became one of their heroes. When the very Jewish Dr. Fleischman starts casually using Yiddish with the local Indians in an attempt to connect with them, he's told (by them) to knock it off because he sounds like a poser.
Babylon 5: Susan Ivanova is Jewish and occasionally uses Yiddish word order and phrases for comedic effect:
The assorted Jewish gangsters of Boardwalk Empire are conversant in Yiddish. Manny Horvitz in particular is fond of it, boychik, though Arnold Rothstein doesn't seem to be.
Then there's the Crowning Moment of Funny from "Broadway Limited", where Prohibition Agents Van Alden and Sebso are interrogating a gravely injured Jewish gangster in the middle of a public dentist's office. He growls something at Van Alden and the nice lady in the corner gasps in shock. Van Alden orders her to translate word for word:
Woman: He says you should fuck your grandmother with your faggot penis.
Sebso: Little faggot penis.
Another interesting use of Yiddish is an exchange between Jewish Meyer Lansky and Italian Lucky Luciano:
Luciano: Meshuge bisl yingl. (Crazy little kid.)
Lansky: Che cose potente fare? (What can you do?)
Luciano does it again, with a side order of Ho Yay, in "Bone for Tuna":
Luciano: You know Masseria hates your [Meyer's] sheyna punim. (pretty face)
On Law & Order: Criminal Intent, Barek asks Logan if he feels like "taking a schvitz" with a suspect. To be fair, Yiddish is one of the languages she picked up while working for the FBI. Logan, on the other hand, is a NYC Irish Catholic.
In an early episode of the Law & Order mothership, Cragen responds to his detectives reporting that their last lead failed to pan out with "What's less than nothing? Minus zero? Negative bupkis?"
In the Two and a Half Men episode "Captain Terry's Spray-On Hair", when Alan pretends to be Jewish so he could use a Jewish dating service, he uses as many Yiddish expressions as he can.
New Girl: Schmidt has spoken of his zayde and his need to pish.