Voting for candidates of the same party for multiple positions is called straight-ticket voting. For instance, if a member of the Democratic Party in the United States votes for every candidate from President, Senator, Representative, Governor, state legislators and those running for local government that is a Democrat, this is considered straight-ticket voting. In general, straight-ticket voting was a very common occurrence up until around the 1960s and 1970s. Since this time, this kind of voting has declined in the United States among the general voting population; however, strong partisans, that is strong party identifiers, have remained straight ticket voters.
In the early days of the parties, it was nearly impossible to not vote on a straight party line vote. To vote, voters would receive a colored ballot with that party's nominees on it. To split ticket vote, you would need two different colored ballots, which made it confusing to the voter. Often, the voter would either choose a specific party, and vote for everyone from that party.
One possible reason straight-ticket voting has declined among the general electorate in past years is the power of incumbency has risen. Also, there are very few places where there still is a one-party rule. In the South after the civil war, the Democrats were completely in power, and the hostility toward Republicans made it that an overwhelming majority of voters voted straight down the line on the Democratic side. Furthermore, local parties tend to run very weak party identifiers for local positions, such as mayor or town council, so at local levels, candidates must actually fight for their votes.