Elections where the winning party lost the popular vote.

[Barnes]

The Georgia Gubernatorial Election of 1966

Lester Maddox (Dem) - 450,626
Bo Callaway (Rep) - 453, 665
Ellis Arnall (Dem, write-in) - 69,025

A bitter Democratic primary between Maddox and Arnall - representing the conservative and liberal wings of the party, respectively - led to Arnall leading an insurgent write-in campaign.  At the same time, Callaway, marking a resurgent Republican Party in Georgia, became the party's first viable candidate for Governor in living memory.

As a result, the three-way contest failed to produce a winner with an overall majority.  At the time, if a candidate failed to win a majority at the election, the General Assembly would choose the governor - much as the federal House of Representatives still does under the electoral college.  

Of course, Democrats made up the overwhelming faction of the legislature at the time and easily chose Maddox as Governor, even though he won 3,000 fewer votes than Callaway.

EDIT: Just remembered that this is technically the International General Discussion board, but I thought this result was too interesting to fail to mention.

[Barnes]

Vermont retains the system to this day, and actually put it in practice last month.  However, I don't know of any time when the second-placed candidate was selected.