The first are the traditional horror exams where you might be tested on your expertise, but you only got a chance to use it if you could remember a whole pile of facts. And I still occasionally get nightmares where I am in exams and can't remember this or that formula.
The other type was pretty much the last exam I ever took, on my OR course at Lancaster. Called a 'jumbo' it was a 6ish hour exam with a single question. (Though admittedly that question was a good few pages long). You could take in whatever books you wanted - and go out and get more if you wanted. Not only was it far more interesting to do than a traditional exam, I believe it told you far more about the candidate than any ordinary test.
I really can't see any reason exams should test memory. Surely they should be about understanding and what you can do with the equations (or history dates or whatever)? I think this also fits very well with the RSA's alternative school curriculum, which is all about giving students the tools to research and work, rather than remembering lots of facts.
How about it, educationalistas? Can we move to a better way?