I'm going to start working on a new project. It's a 3D game using OpenGL for Windows, Linux and Mac OS X. and I'm going to need a library for GUI, windowing and handling input. I ended up with 3 choices Qt, WxWidgets and GTK+. All of them are under LGPL license.
1- Does LGPL allow to use these libraries to make proprietary applications?
2- Which one of these 3 applications is best for me?
Yes, so long as you don't statically link to them (ie: use them as DLLs). Though wxWidgets allows you to statically link without becoming GPL'd.
None of the above. If you are making a 3D game, then none of these is good for your needs. The needs of a GUI for a game are very different from the needs of a GUI for a typical desktop application. In a game, you want you particular GUI elements to be consistent with a particular artistic direction, not be consistent with the desktop environment. Plus, you may want your GUI elements to be more expressive than what these toolkits would normally allow.
It is for reasons like this that CEGUI exists. That is a GUI system designed for the needs of a game.
Also, none of these provide input the way a game generally wants to process it. You typically want something lower level for a game than what these toolkits provide. That's why projects like SDL and SFML exist.