I’ve put together a list of IDEs that can be used for development with Corona SDK. Some of the software recommended on here may have you going “that’s not an IDE! it’s just a text editor!”. Yeah, well…who cares!
Koneki – It’s free and part of the Eclipse product family. This is standalone OR can be integrated with Eclipse.
Notepad++ – Also free. It does NOT have out-of-the-box autocompletion for Lua though. You can achieve that through this, however.
Sublime Text – A very editor. You can try it out for free.
Lua Glider – Corona pushes this product a lot. Why? Because they made it! It’s available for Mac + Windows, has debugger features, and autocompletion for both Lua AND Corona. You can get a trial for this.
ZeroBrane Studio – It’s open-source + cross-platform. It supports debugging with: Löve 2D, Moai, Gideros, Marmalade Quick, Corona, and Cocos2d-x.
Outlaw IDE – Originally called Corona Project Manager and designed for just Corona SDK, this IDE also now supports Moai SDK. There’s a free version, but it has some limitations and also has an ad in it.