There certainly are open source SWF options but I have never tried any of them - I have been using Flash extensively since version 4 and would never bother with anything but the real McCoy.
Although Flash is now almost synonymous with web video (thanks to YouTube) it is capable of much more, including script and database interaction, and while I wouldn't comment on the 95% figure I would say it is pretty safe to assume that anyone visiting a site that offers games is very likely to have it installed.
For animations or "little quizzes" I can't see why you would want video - these things (and much else) can be done in version 5 or 6 of Flash, and you might be able to pick up a cheap copy if the high price of the current version is discouraging you.
Thanks Samizdata for your direct answer. I would still be interested to see hear what other tools people on webmaster world use to make interactive quizzes and so on.
For example: what would you use to create a ten-question quiz (10 questions randomly drawn from a database) with 3 multiple choice options and that gives you a score at the end? Is making something like that pretty simple?
This would be pretty basic stuff in any scripting language - personally I would use PHP with a MySQL database, but what you use would presumably depend on your hosting facilities.
Making a Flash "front end" would also be fairly simple if that is what you want, and has the advantage of processing everything without reloading the page. But the whole thing could easily be done without multimedia, and this question really has nothing to do with video.