Yes, as long as the codebase differs from the cloned project in its implementations. (i.e. You don't directly use code from the original game)
This entirely depends upon the legal copyrights set forth by the original creator.
By default, U.S. copyright law automatically grants copyright ownership to the original creator of the content.
The artwork, sounds (music and effects), narratives, and other such assets can not typically be re-used unless explicitly specified in a license chosen by the original author. An example of non-restrictive licenses for creative assets would be the Creative Commons licenses.
Code for the original game is often licensed separately from the art assets, but has the same set of rules. However, as long as your code base differs significantly in its implementation, it is not generally considered a "copy", and therefore is not in violation of copyright. Much software out there provides similar features of other software, but they differ in specific implementation.
As far as gameplay goes, there are plenty of clones around already, so it's not quite as restricted. Although you may make some people pretty furious if they're protective of their ideas. :-)
Extra reading on copyright laws: http://copyright.gov/
Answered quite a while ago, but some additions are necessary.
I'm not a lawyer
@Josh1Billion is correct regarding patents. They're an entirely different beast. Unlike copyright, which pertains to your specific implementation of code, these will get you for using the general architecture of a concept (and not necessarily with code). @Josh1Billion's comment provides a good example.