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: 
Here's my 10,000 foot view of open source licenses:

"Real" open source licenses (eg: MIT, BSD, Apache I think, etc.):
You can do whatever you want with licensing derived works. It can be closed, open, etc. The license places no restrictions on your licensing of derived works.

"Restricted" open source licenses (eg: GPL, LGPL):
Derived works must include specific license restrictions; for example, the GPL requires derived works to be GPL-ed. Essentially your rights are restricted for derived works.

Charging for products is separate from either of these; neither type restricts charging for products, although some licenses place restrictions on the rights you can retain and/or must convey to receivers of your software (ie: the "Restricted" licenses).

Hope this helps.

Edit: Changed by original "DRM" term for GPL type licenses to "Restricted", cause some people attach negative connotations to DRM, and/or cannot grasp how the GPL restricts your rights for derived works in an almost identical way to any other type of DRM (ie: controlling what you can do with it). Seriously, you can be a FSF supporter and still grok the concept that the GPL is more restrictive than "real" open source licenses. The question is not about which type is right or wrong, it's about what the difference is.
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.