Although US presidents win election based on the electoral college vote, it is interesting to take note of how the popular vote runs.
George Washington could be considered to have won the popular vote by the greatest margin since he ran unopposed and got 100% of the vote but his election is thus not really comparable to the subsequent elections...
Note that the elections probably ought to be divided into 4 periods: Washington, First Party System, Era of Good Feelings, and post-1820.
Additionally it should be remembered that prior to the ratification of the 12th Amendment in June of 1804, the electoral college voted on the president and the runner-up became vice-president. Also popular vote totals in the earliest presidential elections are not strictly comparable to those in later elections since several states really didn't hold a popular vote for president but rather let their legislatures pick the electors for the electoral college.
George Washington was elected with 100% of the popular vote to both of his terms.
After Washington the Federalists clashed with the Democratic-Republicans to become the dominant "First Party" and control national and local politics. Margins of victory during this time were:
1796 53.4% vs 46.6% Adams vs Jefferson
1800 61.4% vs 38.6% Jefferson vs Adams
1804 72.8% vs 27.2% Jefferson vs Pickney
1808 64.7% vs 32.4% Madison vs Pickney
1812 50.4% vs 47.6% Madison vs Clinton
1816 68.2% vs 30.9% Monroe vs King
The "Era of Good Feelings" was marked by the re-election of James Monroe who ran essentially unopposed in 1820 and won 80.61% of the popular vote.
The election of 1824 saw a splintering of politics into multiple parties with no president approaching the previous margins for a long time.
Since 1824 the president who won with the greatest percentage of the popular vote was Lyndon Johnson who, in the 1964 election, won with 61.05% of the popular vote compared to 38.5% for the Republican candidate, Barry Goldwater. Johnson won 486 electoral college votes to Goldwater's 52.
In 1984, Ronald Reagan was elected with 525 electoral votes, the largest number ever won by any US president. This was also the largest percentage of possible electoral votes ever won. However, the electoral vote system was changed in 1872, so the number of electors won by presidents elected prior to 1872 cannot be compared perfectly with the current system.
The greatest percentage margin of victory since 1820 was President Warren G. Harding who won 60.32% of the popular vote compared to 34.1% for the Democratic candidate James Cox. The rest of the popular vote was split between other candidates including Eugene Debs (Socialist - 3.4%), Parley P. Christensen (Farmer-Labor - 1%), Aaron S. Watkins (Prohibition - 0.7%), James E. Ferguson (American - 0.2%) and William Wesley Cox (Socialist Labor - 0.1%).
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All state officials are elected by popular vote.
Electors are elected by popular vote but the president is elected by the electoral college. A president candidate can win the popular vote and still not win if he doesn't win the electoral college.
No US president was elected unanimously by popular vote. The only president elected unanimously by the electoral college was George Washington (There was no popular vote in this election).
legislation
Presidents were never elected by popular vote. They have always be elected by the electors from each state who cast their electoral votes. What has changed is the way that the electors are selected. Nowadays they are chosen by popular vote, but at first the state legislatures would choose them.