At Caltech, they were normally take-home. Institute policy was they were not proctored. The exams had a time limit from opening the exam to pencils down. The conditions, like open-note or open-book, were specified.
The students were totally on their own with this and nobody would know if they chose to cheat or not. Cheating was so trivial to do there was no cred for bragging about it. If other students found out someone was cheating, that someone would be ostracized by the students, which was much worse than anything the institute could do to them.
Of course, people are people and I'm sure some cheating went on. But I bet it was at a much lower rate than at places with proctored exams.
As for me, it was the first time in my life adults trusted me and treated me like an adult rather than a child. I much prefer that to the extended childhood offered by other universities. I was motivated by simple pride to earn the degree rather than cheat and get a tainted one.
I graduated from Caltech last year, and the exams are all still take-home. You're expected to time yourself and not consult course materials, and basically nobody cheats. It's a rare sort of equilibrium where nobody's cheating, so it's very hard to start -- you won't find any co-conspirators, and if you're found out it's social death.
I'm a bit saddened that other universities have not attempted to emulate this. Maybe it only works because Caltech is such a small place, small enough that you get to know most of the people there, and the social interconnectedness is strong.
10 years after Caltech, I went to law school. I was surprised to find that they did not have take home exams. Law is a profession that actually has ethical requirements, but apparently we can't trust law students to behave ethically?
This annoyed me not only because of the lack of trust, but because law school exam questions are almost always essay questions that take a few pages to answer. No way did I want to try handwriting that much.
Fortunately, they did allow you to at least bring a typewriter to the exam (they set aside a separate room for this so it would not disturb the people who were handwriting).
There were limits, though. The typewriter could not have more than 2 lines of storage. This was around 1992, and already by then microprocessors and LCDs had become cheap enough that even most entry level typewriters exceeded the limit. It took a fair bit of effort to find one that was acceptable.
