Finally I've come across a source listing those states that allow straight-ticket voting, where a single mark casts votes for all the candidates of the chosen party. The Hill newspaper has an article regarding a bill to ban the practice. FYI, those 15 states are: Alabama, Indiana, Iowa, Kentucky, Michigan, New Jersey, New Mexico, North Carolina, Oklahoma, Pennsylvania, Rhode Island, South Carolina, Texas, Utah and West Virginia.
The ability to vote a straight ticket is a legacy of the party machines that wanted to make it easy for voters to support the full slate. As far as I remember, my home state of Colorado never had the provision.
I don't feel strongly about forbidding the practice. There are such more important electoral reforms the federal government should be pushing, such as increasing the number of polling sites to avoid the long lines and increasing days for registration and voting.
Another legacy practice, in Virginia at least, is the failure to list part affiliation on the ballot -- because the pro-segregationist Virginia Democratic party in the 1960s didn't want to be hurt by linkage to the pro-civil rights national Democratic party. I don't think that should be required nationally either.