First, rubrics are most appropriate for performance-based assignments. These are assignments where students are asked to do something, something like write a paper, give a presentation, or complete an experiment. Assignments where rubrics are appropriate almost always involve students applying learning or thinking in new situations. You would not want to use a rubric for every assignment you give students.
On a more personal note, you might find rubrics particularly helpful when you find yourself writing the same comments over and over, you’re dismayed at how long it takes to grade (performance-based) assignments, or you suspect you’re grading papers at the end of the pile differently than you did at the beginning. A good rubric won’t turn essay grading into a speedy activity, but it will save you some time. And it can help you grade more consistently than you might without it.
Rubrics are also often appropriate when there seems to be a mismatch between your expectations and students’ work, when you thought you were perfectly clear in your assignment directions but the work students hand in seems like it came from a different assignment than the one you gave them. Rubrics help students understand what you expect–and the clearer your expectations, the more likely students are to fulfill them.