Sploder is a website that offers free tools for creating your own video games. There are four basic game templates that you can modify to your heart's content. The four templates are a physics puzzle game, an algorithm creator (which reminded me a little of Zelda), a shooter game template, and a blank platform which I used to create a simple Mario Brothers-like game.
Creating games on the Sploder platform is a drag and drop process. You can select as many elements as like for each scene of your game. Game elements can be resized and re-used repeatedly throughout your games. When you think you're ready to publish your game, use the Sploder game tester to try your game and see how it actually works. If you find something you want to change in your game, you can do that at anytime after testing it and before publishing your final product.
Sploder has a YouTube channel containing some tutorials to walk you through creating games. I've embedded one of the tutorials below.
Applications for Education
Creating a game on Sploder could be a good way to get students to think about the logic and sequencing used to plan and develop video games.