For some upper level classes, though, a 2-3 hour exam really isn't enough to ask them the kind of in-depth question I want to ask. Abstract Algebra comes to mind. In those classes I will give a take-home exam, although I sometimes pair it with a short in-class exam to test basic concepts. I have mixed feelings about this. Often the take-home exam works very well, but twice there have been suspicions of cheating, and there's not much I can do about that -- even talking to the student carries consequences (I have talked to the students in both cases, but the first time I wasn't as careful about how I presented my concerns and I think it hurt our relationship in the long-term. Since I didn't have anything close to proof, I'm now not sure I should have even talked to her.). In order to minimize cheating I try to limit the amount of time they have to 1-2 days, and they're not allowed to talk at all about the exams to others, even whether they've finished a problem or not. They find the not-talking to be the most challenging!

Incidentally, while my finals are a little longer than my in-class exams, I tend to give the same kind of final as I gave mid-term (in-class or take-home). The only exception is that sometimes I don't allow an index card on the mid-terms, but I do for the final because the final is cumulative. And finals typically account for 20-35% of the grade in the class, with homework, exams, papers, or projects making up the rest.