I never seem to be able to find a good free quiz site when I want one. I admit that’s not very often since I tend not to do a lot of quizzes, and, due to lack of computer time, most get done on paper. Despite that, the Wild Apricot Blog has produced a pretty good list of tools to create your own quizzes. Some of the sites I know, but one or two I’ve never heard of before but they look pretty good. Not all sites are free. Some give you a taste for a limited time, hoping to drag you into their paid services when your trial period is over.
If your purpose for the quizzing is for studying or self-testing, I might also suggest Quizlet which is great for flash card style studying. It’s pretty easy to set up the flash cards, and the great part is that the kids can’t lose them. While they also can’t study on the bus on the way to school, Quizlet will let you print off the material you inputted so you can make your own non-virtual flash cars.