Here are some of the Frameworks we have come across so far.
App Inventor – This is for Android only and I think created by Google.
Mono – There seems to be 2 version of this software, 1 for iOS and 1 for Android. What I like about the look of this you can use ASP.Net code to develop iOS apps.
GameSalad – This is for iOS and I think Mac games (also Android with the professional version). Had a little play with this and it looks really good. There is no programming knowledge needed for GameSalad, it’s more of a package you have to learn.
Corona – This is what we are using at the moment. Language used is Lua and so far we are finding it really good.
Gideros Mobile – Language used is Lua and looks like it’s FREE if you don’t mind a splash screen before your app loads.
Moai – Also uses Lua as the scripting language. Again this FREE to start with and then you can upgrade to a pay monthly package.
Kobold 2D – Also uses Lua as the scripting language. This is FREE as far as we can see as there is no mention of prices.
Lime JS , Impact JS – These are both HTML 5 game frameworks, so you develop the game in HTML 5 and it will run in a browser but you can run a convertor on it to convert it to a full iOS app and submit it to the App Store.
jQuery Mobile – Another mobile framework based on jQuery.
There are probably loads more we haven’t even found yet.