Still trying to find a state electoral college that went against the popular vote of that state, or it's proportional allocation.
Four times:
In 1824 Andrew Jackson received a plurality of the popular (inasmuch as we actually have records of it at that time) and the electoral vote, but was not elected President.
In 1876, Samuel Tilden beat Rutherford B. Hayes by 3% in the popular vote, and lost the EC by 1 vote -- Louisiana, Florida, and South Carolina were all extremely close, and the board appointed to examine them was composed of 7 Dems, 7 Reps, and 1 Independent; however, the Independent resigned and was replaced by a Republican, so the board ruled that all three states had voted for Hayes.
In 1888, Grover Cleveland was the incumbent President, and barely lost his home state and the election to Benjamin Harrison, who lost the popular vote by less than 1%.
And I think we all remember what happened in 2000.
In addition, there have been quite a few elections in which a few dozen thousand votes could have been switched in key states and changed the outcome of the election: Kennedy beat Nixon 303 to 219 in the EC, but got barely more than a hundred thousand popular votes more, and Nixon beat Humphrey 301 to 191, but got only half a million more votes. Nixon could have won Texas and Illinois without winning the popular vote, and Humphrey could have done the same with Missouri, New Jersey, and Ohio.