This post will be a running aggregation of pending "natural born citizen" challenges in the 2016 presidential election. Please feel free to post updates in the comments about other pending challenges.
The bulk of challenges center around Senator Ted Cruz, born in Canada to a Cuban father an an American mother. There are other challenges (including those regarding Bobby Jindal, Marco Rubio, and Rick Santorum), but they are more obscure (indeed, Messrs. Jindal and Santorum have dropped out). Additionally, there are administrative challenges to candidates' eligibility to appear in a primary (e.g., whether Donald Trump is a "Republican" or whether Bernie Sanders is a "Democrat") or whether candidates have met the ballot access requirements (e.g., whether a candidate has met the requisite number of signatures to appear on the ballot). Those are not included below.
Please feel free to include updates or links in the comments below, or contact me via Twitter.
An * preceding the case means a final judgment has not yet been entered.
Board of Election or Secretary of State Administrative Challenges
Illinois, State Board of Elections (coverage here)
Joyce v. Cruz (160SOEBGP526), Graham v. Cruz (16SOEBGP527), Graham v. Rubio (16SOEBGP528): decision
Indiana, Election Commission
Carter v. Rubio (Cause 2016-2), Carter v. Cruz (Cause 2016-3), Kern v. Cruz (Cause 2016-4): decision permitting appearance on ballot, not yet available electronically, news story here
New Hampshire, Ballot Law Commission (coverage here and here)
Elliot v. Cruz, Booth v. Cruz (BLC 2015-2): decision
Laity v. Cruz, Laity v. Rubio (BLC 2015-4): decision
New Jersey
Williams v. Cruz (OAL STE 5016-16), Powers v. Cruz (OAL STE 5018-16): recommendation, adopted
New York, Board of Elections
Fischer v. Cruz, Gallo v. Cruz, Laity v. Cruz: not yet available electronically, news stories here and here; filing; decision permitting appearance on ballot (archived webcast)
Litigation
Federal
Green v. Cruz (N.D. Ala. 5:16-cv-207): complaint, amended complaint; dismissed without prejudice (May 10, 2016)
Librace v. Martin (E.D. Ark. 4:16-cv-57): complaint, dismissed (Feb. 29, 2016)
Booth v. Cruz (D.N.H. 15–cv–518): dismissed (Feb. 2, 2016)
Fischer v. Cruz (E.D.N.Y. 2:16-cv-01224): complaint, dismissed (Apr. 7, 2016)
Schwartz v. Cruz (S.D. Tex. 4:16-cv-00106): second amended complaint; dismissed (April 13, 2016); summarily affirmed (5th Cir. 16-20231)
Wagner v. Cruz (D. Utah 2:16-cv-00055): complaint , dismissed (Mar. 18, 2016); affirmed (10th Cir. 16-4044); petition for writ of ceriorari (15-1243), denied (May 31, 2016)
State
Voeltz v. Cruz (Broward County, Fla. Circuit Ct. CACE15022044): docket, dismissed (March 4, 2016)
Smallwood v. State (Hawaii Supreme Ct. SCEC–16–0000330): dismissed (Apr. 21, 2016)
Joyce v. Cruz (Illinois): not yet available electronically, news stories here and here, dismissed (Mar. 1, 2016)
Korman v. New York State Board of Elections (New York County, Supreme Ct. 100240/2016): memorandum of law; dismissed (Mar. 7, 2016); affirmed on appeal (Mar. 24, 2016); appeal denied (Mo. No. 2016-374, Apr. 1, 2016)
Laity v. New York (New York), dismissal affirmed on appeal (Aug. 10, 2017); petition for writ of certiorari filed, (No. 17-1007, Jan. 19, 2018)
Farrell v. Cruz (Pennsylvania): dismissed (Mar. 11, 2016), news stories here and here; appeals to Supreme Court (29 MAP 2016), affirmed (Mar. 31, 2016); petition for certiorari sub nom. Elliott v. Cruz (16-13), denied (Oct. 3, 2016)
Paige v. Vermont (Washington Civil Div., Vt. Sup. Ct. 780-12-15 Wncv): complaint; dismissed (May 12, 2016); appeal to Supreme Court (2016-202), dismissed (June 16, 2017).