Which presidents failed to win the electoral votes but still won the presidency?

This only happened twice, In 1800 when Thomas Jefferson was elected, he and his running mate, Aaron Burr tied in electoral vote. After a lot of debate, Jefferson was elected by the House.

In 1824, when John Quincy Adams was elected by the House, Andrew Jackson led in electoral vote, with Adams second, but the house chose Adams.

(In 1876, it almost happened when disputes over the credentials of electors arose, but a special panel settled the dispute by giving all the disputed electors to Hayes who won by one vote.)