1. Construct 2 (2D)
With Construct 2, you can easily make 2D web-based game, without coding! To start, follow the tutorial http://www.scirra.com/tutorials/37/beginners-guide-to-construct-2
The basic version is free. The personal version with more features is 49 EURO, and the business version is 229 EURO.
2. Unity3D (3D):
With Unity3D, you can make 3D games that can be played on the web, iphone, ipad, android platforms, and desktops. The best place to start is to follow tutorials on http://cgcookie.com/unity/getting-started-with-unity/
The basic version is free. The iOS and android plugins are available (not free).
Unity iOS Plugin: $499
Unity Android Plugin: $499
Unity Flash Plugin: $499
Unity Pro: $1500
Unity Pro iOS Plugin: $1500
Unity Pro Android Plugin: $1500
Unity Pro Flash Plugin: $1500
3. jMonkey (3D)
jMonkey is a Java-based game engine and IDE, based on NetBeans platform. To install, go to http://jmonkeyengine.com/
To start, follow the tutorials http://jmonkeyengine.org/wiki/doku.php/jme3#tutorials_for_beginners
jMonkey is free and is an Open Source project.