Playcrafter is a site where you can create your own game. Accounts on the system are free, and allow you to make and save your own games. There is also a paid level of account that will let you make games with more than 10 levels and some other features.
Games made with Playcrafter can be embedded into web pages, and can also be run on devices that are Flash 9+ friendly.
If you try this out with your students or kids, let us know about it in the comments.