People have already covered Game Maker. But there is also another engine which can produce similar results to Game Maker called Construct 2 (
https://www.scirra.com). I quite like it, though I also like Game Maker. Here are the advantages and disadvantages of Construct 2 over Game Maker:
Advantages:
Easier to use
Can be cheaper if you are making a mobile game, as you don't have to pay extra
Doesn't charge you for each new version, or as much
Disadvantages:
May not be quite as powerful (theory)
Is not as fast as Game Maker
Making mobile games on it can be just a little iffy, though people have done it before