LÖVE is an awesome framework you can use to make 2D games in Lua. It's free, open-source, and works on Windows, Mac OS X and Linux.
Pro Very good documentation
The LÖVE wiki provides full documentation of its easy to use Modules, which are conveniently located on the side bar of the wiki. It took seconds to find the module for love.keyboard, which provided a list of all functions along with arguments and examples where the function could be used.
Pro Active and very friendly community
The LÖVE forums are extremely helpful. With people checking the forums every day, it won't take long to receive answer to your questions on the Support board, receive feedback on games you post in the Projects board, as well as have a chat about the LÖVE engine while learning tricks to use in the very active General board.
If you need an immediate answer though, or just want to chat, there is a very active and helpful IRC channel.
Pro Uses the fantastic Lua for scripting
Lua is an embeddable scripting language designed to be lightweight, fast yet powerful. It is used in major titles such as Civilization as well as a lot of indie games.
Lua is very popular because it provides "meta language" features. You can implement object-oriented structures, or pure procedural functions, etc. It has a very simple C interface, and gives the engine developer a lot of flexibility in the language itself.
Artists tend to love Lua too because it's very approachable, with plain and forgiving syntax.
Lua is free open-source software, distributed under a very liberal license (the well-known MIT license).
Pro Simple to use/understand
Lua2D handles loading the resources, reading input, playing sounds and displaying stuff on the screen. Only the logic is left for the developer to write. It also removes the overhead of having to use and learn a GUI game editor. All you need is a knowledge of Lua and your favourite text editor or IDE.
Pro Open source and free
The LÖVE engine is licensed under The zlib/libpng License (which is very short and human readable) which allows you to use the source code and even modify it as long as you do not claim that the original source code is yours.
You can obtain the code at this bitbucket repository and even help fix bugs and participate in the development of LÖVE.