If I make a scene and then render it with BR or Cycles, am I allowed to use that image in a commercial project? Do I need to include any copyright notice or license?
Short answer Yes,
Just as you own what you draw with a pencil, you own works you make with Blender (no difference).
Copied from blender.org
Meaning anything you make in blender (images, scripts, addons, models, entire scenes, materials, textures, and so on) is yours, and you can do anything with it, without any legal notices at all.
The one exception is standalone executables of games created with the BGE (because this includes Blender's own runtime). See the FAQ for details.
To expand a bit on David's answer -
The GPL license used by blender is applied to the source code used to create blender, it only forces you to share modifications you make to the source code if you create a modified version of blender that you wish to share.
The GPL does not effect the data (the blend files) used by blender or output generated (our artwork) by blender.
The data and artwork you generate when using blender is fully owned by you and you can choose to use or share it under any terms you wish.
Similarly you will also find that most of the data used to create the open movies created by the Blender Institute are released under the Creative Commons Attribution license (CC-by), this means you are free to use the models used for the short movies as long as you give credit for their creation "by The Blender Foundation" and not claim them as your own.
Disclaimer - this is an explanation of my understanding and not to be taken as legal advise. Get proper legal advise if you are unsure of how the licensing terms affect your usage.