I know that Blender.org provides downloads for official releases. I see on forums that people use newer versions of Blender. Where can I get newer version of Blender (nightly builds, alpha versions... etc).
You can get daily builds for Linux, Windows and Mac from graphicall.org. Here you can also find GSOC and custom builds (Yafaray, Luxrender support etc).
Compile from source:
Another option is compiling blender from source, see the wiki. While this may seem like a lot of effort, once its setup, it can be less trouble then having to continually download large files, and you can test new features minutes after they're committed.
You can get past releases and current test-builds/release candidates here.
There are some additional options for linux besides GraphicAll.org and the ones listed above.
You can get official daily builds here https://builder.blender.org/download/