6th President of the United States John Quincy Adams came out of retirement to serve as a member of the U.S. House of Representatives from 1830 to his death in 1848, representing his home state of Massachusetts. 17th President of the United States Andrew Johnson also served as a Senator for Tennessee in 1875, before dying several months into his term.

Reference

Biographical Directory of the United States Congress, entries for Adams, John Quincy and Johnson, Andrew.

Martin Van Buren ran for president again, twice. He was voted out in 1840, after being tarred at Martin Van Ruin for the Panic of 1837. He tried again in 1844, but his own party turned on him that time. One of the big issues then was that he didn't go all-in for the annexation of Texas, which made him insufficiently sound on slavery. Even with that, he had a flat majority of the delegates at the party convention. The rules just required 2/3, which gave the South veto power over the presidential ticket.

Van Buren was steamed and he had enough followers that he gave it a third go in 1848, this time running on the Free Soil ticket. The free soilers were a third party movement opposing the expansion of slavery. Van Buren and his people weren't the only players in the coalition, but the others shifted somewhat to accommodate them. This time around, he came in third.