John Tyler's veto, early in his presidency, of a bill to establish a third bank of the United States, effectively alienated him from the Whig Party (he had been elected on the Whig ticket, mostly to offer geographic balance). But Congress wasn't able to override that or four other of his vetoes. On the last day of his term, March 3, 1845, Congress finally overrode Tyler's veto of a relatively minor naval appropriations bill. To use a more modern phrasing, it was Congress' way of giving the finger to a president they disliked, a small jab at the moment when Tyler was celebrating the passage, and his signing on March 1, of the joint resolution annexing Texas.
The all-time veto champ among the presidents, not surprisingly, is Franklin Roosevelt, who in over 12 years used the veto 635 times, 372 regular and 263 pocket. Only nine were overridden. Among two-term presidents, Grover Cleveland had the highest number of vetoes, proportionally more than FDR: 584 of both kinds, with seven overridden. Andrew Johnson, whom Congress hated and who hated Congress, had the most overrides: 15 out of 29 vetoes.