That was the campaign slogan for William Harrison and John Tyler during the Election of 1840. It refers to Harrison's leadership as Governor of Indiana during the Battle of Tippecanoe in 1811.
It's not clear that any one party became known for this, since the practice evolved over time. But one of the earliest (and most successful) campaign slogans that we know about goes back to 1840, and the Whig party. The Whigs used the slogan "Tippecanoe and Tyler Too" to promote William Henry Harrison, whose nickname came about when he was a military officer who won a great victory at the Tippecanoe River in the Indiana Territory. His running mate was John Tyler, and thus the slogan.
John Tyler
MentoS :)
This is an old slogan for Band-Aid.
The Australian telecommunications company Optus has "Yes" as its slogan.
My nomination for this dubious distinction goes to Chester A. Arthur, who was not elected and could not get his party's nomination to run as the incumbent president. Others might choose William Henry Harrison who served for only one month or Warren Harding who did not complete his term and whose administration was tainted with scandals. I think the slogan, "Tippecanoe and Tyler too" keeps Harrison from being totally forgettable and Harding was too bad to be forgettable.
VXC
Palmolive
Rolaids.
Oracle.
7-Up
United Airlines used this slogan in the past.