Professor Jim Heffernan routinely asks his students to write short personal response essays on the reading they've done for class. The only requirement that this professor makes is that students must begin their essays by quoting some part of the text they've read. This one requirement forces students to consider more than their own feelings about the text. At the very least, they'll have to consider why they chose this particular passage to respond to. Ask students to analyze their personal writing.
Some professors ask students to write personal essays about a particular topic.
Then, after reading some critical or scholarly works about that topic, students are asked to return to their personal essays and then to analyze them according to what they've read or talked about in class. This exercise teaches students to think critically about their own experiences and responses, deepening their analytical skills. Ask students to write a personal essay, and then frame that essay with an introduction and conclusion that are analytical. Assign journals, and ask students to use their journal as a resource for at least one of their academic papers. Journals are an excellent way to make room for the personal in your course.