Question: This question has always been around my head.

Can someone create a new product based on an existing open source project?

Say you want to create an "Apaxe webserver" that is basically Apache with your some extra plugins ( say support for ASP or something similar ) 

Is this possible?

Would you be able to create a closed source product ( either free or licensed ) 

As for GPL seems clear it is not possible because the source should be open. But what about Apache license, BSD and others "corporate friendly"

Are the price ( free for most of the project ) , bug fixes and counting with the core development team the only thing that prevent from others to commercialize those OS products?

What about: Khrome a commercial product based on Chrome with ActiveX support ( who would dare to do such a thing :P )

**EDIT**

Thank you all you all for your answers. 

So, again

***What prevents from similar ( clone ) products from appearing in the market?***

:) 

NOTE: I know we are not lawyers, and we could read every OSS license here <http://www.opensource.org/licenses>.

Answer: 
Generally, my read of the licenses is:

1. You can make a derivative work of any project based on one of the popular licenses (i.e. GPL, LGPL, Apache, MIT, BSD).
2. You may charge money for at least the distribution & packaging of your derivative work.
3. Depending on the license, you may also have to distribute your modifications in source form and/or include notices in your distribution.

So to your question about Apaxe: yes, you can do this as far as I know. I believe that the Oracle HTTPD server is actually derived from Apache, and it's definitely not free!
Isn't that essentially what red hat does? Even though they have fedora, they are charging money for their linux distribution. Granted, they've written a lot of code for it, it's still based on open source-stuff.