Third party candidates impacted elections in 1948, 1960, 1968, 1980, 1992, 1996, and 2000. That's seven of the fourteen Presidential Elections in over a half century, including four of the last six and the last three in a row.
The Democrats have won six of the fourteen in that time, and on four of those occasions -- Truman ('48), Kennedy ('60), Clinton ('92), and Clinton ('96) -- they won by a plurality. That means that the Democrats won the Presidency on four occasions when the Republicans plus third parties outpolled them. In fact, only Johnson ('64) and Carter ('76) have gotten more than 50% of the popular vote for the Democrats since FDR's final victory in 1944.
In contrast, of the eight Presidential Elections that the GOP has won in that time, only Nixon ('68) and President Bush (2000) won with less than a majority of the popular vote.
In recent electoral history, third parties are quite likely to impact Presidential elections.