The optimum quizzing environment is one where a teacher can supervise the learner and explain where they are going wrong. It is difficult to get a computer to recreate this, as computers do not understand the subject. There is a significant challenge in getting computers to conjugate and mark quiz questions.
Computer quizzing is effective for mulitple choice, which is particularly good at teaching the lexicon of a subject area; touchtyping is taught well by computer programs (as long as the user does not cheat with what finger they are using on what keys).
Maths problems can work, but if the learner get's the wrong answer, it's would be difficult for the computer to give the learner marks for their workings. One possible solution to this, would be to force the learner to build their workings using a set of tools in the program. This way the computer could analyse at which step in the solution the learner went wrong.
For teaching musical instruments, a computer could ask for a note at random, and measure pitch of the response to ensure the correct note was played. The quicker the user plays the correct note, the better the score. For learning a stringed instrument, the computer to set both the string, hand position and finger to be used (the computer would be able to determine the string used via the timbre of the sound).
Images are an effective learning tool that can be used in a couple of ways: the learner can be asked to click on an area of the image that corresponds to a particular definition (e.g. click on the USA on a map of the world; click on Arizona on a map of the USA). The learner can be shown an image with a label, and can select from mulitple choice the correct answer for that label (e.g. the label points at the hard disk on an image of the inside of a computer, and the learner can pick from "hard disk", "CPU", "RAM", "PSU", etc).
Are all possible quiz types built and out there? Or is there still opportunity?