Some, especially in the mainstream media, pretend that not Jerusalem but Tel Aviv serves as the capital of Israel. (Tel Aviv hosts the Ministry of Defense but not much else of the central government.)
Comments: (1) This absurdity parallels a tendency lately to pretend there's a country called Palestine.(2) For an amusing skit on this topic, see Honest Reporting's YouTube mock-umentary, "Searching for Israel's Capital.
The weblog entry documents some of those delusions in reverse chronological order:
L'Eredità: In a more absurd version of the Argentine game show fracas, Flavio Insinna, an Italian court, the Tribunale di Roma, two days ago ordered the host of an Italian television program, L'Eredità, to state on his next show: "International law does not recognize Jerusalem as the capital of the State of Israel." The Palestine Chronicle explains:
The story goes back to May 21, when a TV game show contestant was asked what is the capital of Israel. The answer "Tel Aviv" was deemed wrong. The right answer, the contestant was told, is "Jerusalem." ...
Italian lawyers Fausto Gianelli and Dario Rossi, representing "Associazione Palestinesi in Italia" and "Associazione benefica di solidarietà con il popolo Palestinese" respectively, decided to take the case to court. After deliberation, judge Cecilia Pratesi conveyed the much-anticipated ruling: "The Italian State does not recognize Jerusalem as Israel's capital."
And then followed the court order to make the statement. Comment: I wonder why the judge did not add that Tel Aviv is the capital of Israel. (August 7, 2020)
"La Tribuna de Guido,"an Argentine trivia game show, breaks the pattern. It asked contestants, "Tel Aviv is the capital of which country?" Reports Israel Hayom: "After one contestant said she didn't know, the other said that while Israel is probably what he should say, that is not the correct answer because Jerusalem is the real capital. Eventually, after a commercial break, a judge in the show said the question had to be struck down. 'Tel Aviv is an important city in Israel and the foreign embassies are stationed there, but the government agencies are based in Jerusalem and that is therefore the legitimate capital city'." (March 12, 2018)
James Mattis: In his confirmation hearing before the Senate Armed Services Committee, asked if he supported moving the U.S. embassy to Jerusalem, retired Marine Corps general James Mattis replied: "Right now I stick with the current US policy. ... The capital of Israel that I go to, sir, is Tel Aviv, sir, because that's where all their government people are."
Comments: (1) Mattis is in error; it is not U.S. policy that Tel Aviv is the capital of Israel. (2) The part about "government people" refers to the fact that the ministry of defense is headquartered in the Kirya ("campus") in Tel Aviv. (January 13, 2017)
The Czech education ministry, under Palestinian pressure, has ordered that textbooks will henceforth refer to Tel Aviv as Israel's capital. (August 31, 2016)
SkySports refers to a soccer game moved from Israel's capital, Tel Aviv. (November 7, 2014)
The Washington Post writes that Israeli "airstrikes raised tensions directly between Tel Aviv and Damascus." (March 19, 2014) Update: The Post corrected the above to "Jerusalem."
Agence France Press: An article on Jan. 23, "Israel PM urges European 'fairness' in Mideast," states that four European Union states lodged "a formal protest against Tel Aviv's drive to expand settlements on the West Bank." (January 26, 2014)
Institut d'Etudes Politiques de Paris (known as SciencesPo): a pro-Israel student cultural organization at this prestigious school goes by the name "Paris Tel-Aviv." (October 30, 2013)
The New York Times: A front-page headline today over a story by Mark Landler and Jodi Rudoren uses "Tel Aviv" as a synonym for Israel's capital: "Mideast Chaos Grows as U.S. Focuses on Israel—Kerry's Tel Aviv Push Raises Questions About Priorities." (July 2, 2013)
CTV, a Canadian television station: Reported on Jan. 8 that "Tel Aviv is dealing with a heavy rain situation. The storms flooded roads and brought chaos to the Israeli capital." (January 17, 2013)
British Broadcasting Corporation: A BBC tweet today announced that "#Gaza militants launch missiles at Tel Aviv in 1st rocket attack on Israeli capital since 1991 Gulf War bbc.in/QJkWK9" (November 15, 2012)

White House: The White House press secretary, Jay Carney, did not say that Tel Aviv was the capital. But he also did not say it was not in this semi-comical exchange with reporters:
1st Reporter: What city does this Administration consider to be the capital of Israel? Jerusalem or Tel Aviv?
White House press secretary Jay Carney fields a tough question about the capital of Israel.
Carney: Um ... I haven't had that question in a while. Our position has not changed. Can we, uh ...
1st Reporter: What is the capital?
Carney: You know our position.
1st Reporter: I don't.
2nd Reporter: No, no. She doesn't know, that's why she asked.
Carney: She does know.
1st Reporter: I don't.
2nd Reporter: She does not know. She just said that she does not know. I don't know.
Carney: We have long, lets not call on ...
2nd Reporter: Tel Aviv or Jerusalem?
Carney: You know the answer to that.
2nd Reporter: I don't know the answer. We don't know the answer. Could you just give us an answer? What do you recognize? What does the administration recognize?
Carney: Our position has not changed.
2nd Reporter: What position?
Carney ignored him and moved on to another question. (July 26, 2012) Feb. 10, 2014 update: Les Kinsolving has named Connie Lawn as the "1st reporter" above and identified himself as the "2nd reporter."
The Guardian newspaper: Its style sheet states that "Jerusalem is not the capital of Israel; Tel Aviv is." (April 25, 2012)