I think there's some confusion of terminology here. If I'm reading right, I think what zhenzhen might mean by "department" and "program" is field/discipline, i.e. you apply to the program at the "library science department" at several universities.
If that's it, you're right that it's most common for people to apply to graduate programs at several universities but in only one field/subject/discipline. It's not that unusual, though, to apply to programs in different disciplines; given someone's interests they might apply to, say, some English departments and some comparative literature departments.
That's what I meant. Thanks for clarifying.