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
To quote from blender.org
Meaning anything you make in Blender (images, scripts, add-ons, models, entire scenes, materials, textures, and so on) is yours, and you can do anything with it, without any legal notices at all.
A general note about Open-Source, not specific to Blender.
You don't have to get into details of each license.
Any OSI approved License assured you can do what you like with works created from OpenSource software. This is part of the Open-Source, definition as defined by the OSI, http://opensource.org/osd
Points 5 and 6.
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.
Blender is a Free tool, Open Source and free, you choose what you do with it, this doesn't mean that you can copy someone else's artwork, If you draw a character with copyrights using a pencil, and use this drawing in a commercial, this is illegal, but it's not the pencil that's going to sue you, it's the entity that holds copyright of that character. So as David said, Blender is a free tool, just like a free pencil, it belongs to everyone who wishes to use, what you do with it, is your responsibility.
[NOTE: I am not a lawyer on any part of the internet, including especially, Blender Stack exchange, nor in any other jurisdiction, and what I write following is a statement of my own personal, informed, but non-professional opinion]
I see a deficit in both Sambler's and David's answers. If you want to use Blender to create an infringing work—Blender models of Thomas the Tank, Mickey Mouse, and model of a French's mustard bottle are but three of a myriad of infringing works—you must first have permission of the everyone who controls the various intellectual property rights to that object. Without prior permission from the IP rights holders, the Blender license does not convey any shield or indemnity against infringement. And in the event of infringement, sambler's statement,
is also likely to be false.
So I'd submit that David's "short answer" should be changed from "yes" to maybe.