This is an especially difficult page to keep updated because of the number of lies Trump is alleged to have made. In addition to some of the whoppers listed on this page, you may want to research some of the other generally available lists which include:
March 13, 2016 Update
Pants on Fire
During the GOP presidential debate Trump claimed that he had never lobbied Florida for gambling.
FACT: He did lobby for gambling in Florida.
(1) Jeremy Diamond, "Jeb Bush: The man who killed Trump's casino dreams," CNN Politics, Sept. 1, 2015, http://www.cnn.com/2015/09/01/politics/donald-trump-jeb-bush-gambling-casinos-florida/index.html
(2) Linda Qiu, "Jeb Bush said Donald Trump wanted casino gambling in Florida, got told 'no,'" Politifact, http://www.politifact.com/florida/statements/2015/sep/16/jeb-bush/jeb-bush-said-donald-trump-wanted-casino-gambling-/ ("...there’s a pile of evidence that Trump was pursuing a deal to operate casinos on Seminole land in Florida.")
Trump has repeatedly maintained that his campaign is self-funded.
FACT: Trump solicits donations on his website and has joined forces with Newsmax Media to do email solicitation, and credible sources report that Trump solicited major donors and had some contact with a Super PAC.
(1) Josh Voorhees, "Donald Trump is Not Self-Funding His Campaign Like He Wants You to Believe," Slate, Oct. 19, 2015, http://www.slate.com/blogs/the_slatest/2015/10/19/donald_trump_has_an_unofficial_super_pac.html
(2) Julie Bykowicz, "News Guide: Trump no longer self-funded, Democrats dominate presidential fundraising," U.S. News & World Reports, Oct. 16, 2015.
(3) Martea Gold and Tom Hamburger, "New ties emerge between Trupm operation and super PAC," Washington Post, Oct. 20, 2015, https://www.washingtonpost.com/politics/new-ties-emerge-between-trump-operation-and-super-pac/2015/10/20/80e7450a-7753-11e5-bc80-9091021aeb69_story.html
(4) Martea Gold and Tom Hamburger, "The inside story of Trump campaign's connections to a big-money super PAC," Washington Post, Oct. 18, 2015, https://www.washingtonpost.com/politics/the-inside-story-of-donald-trumps-connections-to-a-big-money-super-pac/2015/10/18/532b61d4-72b5-11e5-8248-98e0f5a2e830_story.html
(5) Cheri Jacobus, "Trump does have a SuperPAC. and his campaign manager openly discussed it at mtgs w/ me at Trump Tower in May & June," Twitter, Oct. 20, 2015.
(6) -, "Trump sought support from major pro-Israel givers Sheldon Adelson, Paul Singer," Jewish Telegraphic Agency, Nov. 5, 2015, http://www.jta.org/2015/11/05/news-opinion/politics/trump-sought-support-from-major-pro-israel-givers-sheldon-adelson-paul-singer
Trump claimed that his efforts resulted in Ford agreeing to build plant in US instead of Mexico.
FACT: Ford had long-standing plans to build two plants in Mexico and is going ahead with those plans. Moving some assembly work to Ohio had been decided and announced well before Trump tried to take credit.
(1) Robert Farley, "Trump's Bogus Boast on Ford," FactCheck.Org, October 26, 2015, http://www.factcheck.org/2015/10/trumps-bogus-boast-on-ford/ (Ford changed no plans,
(2) Sam Frizell, "Ford Refutes Donald Trump's Claims on Mexico Plant, Time, Oct. 26, 2015, http://time.com/4087058/donald-trump-ford/
During MSNBC GOP debate, Trump denied saying that Rubio was Zuckerber'g personal senator.
FACT: The statement that Rubio was Zuckerberg's personal senator was taken from Trump's own campaign website.
(1) Nick Penzenstadler, "Trump denies calling Rubio 'Mark Zuckerberg's personal senator," OnPolitics, Oct. 28, 2015, http://onpolitics.usatoday.com/2015/10/28/donald-trump-mark-zuckerberg-rubio/
(2) John Santucci, "Despite Denial, Donald Trump Did Call Marco Rubio the 'Personal Senator' of Mark Zuckerbert, ABC News, Oct. 28, 2015, http://abcnews.go.com/Politics/denial-donald-trump-call-marco-rubio-personal-senator/story?id=34792875