Lets say John's Widget Corporation holds a year 2000 patent which
claims that you mix A, B, and C together to achieve goal Z. Then, in
2006, Jill's Widget Corporation applies for a patent which claims you
mix only A & C together to achieve goal Z. May John's Wiget
Corporation have to stop making their product at the demand of Jill's
Widget Corporation, or vice versa, or do both patents still hold
validity?

According to my research, both patents could be valid, but John may be
able to prevent Jill from making Z using her process for the duration
of his patent.

John's Widget Corp. is secure in its patent unless Jill's Widget Corp.
is able to get John's patent declared invalid or unenforceable.  The
last source below will provide you with some insight into how she
might go about doing that.  Otherwise, while Jill's patent may be
perfectly valid, John may nonetheless be able to prevent her from
making her invention until his patent expires if he can get a federal
court to agree that her patent infringes upon his.  The United States
Patent and Trademark Office states that it does not determine if an
invention sought to be patented infringes upon any prior patent. 
Therefore, it is possible for an improvement to an existing invention
to be validly patented while nonetheless infringing upon the patent
for the existing invention.

Sincerely,

Wonko

Sources:

"The Office has no jurisdiction over questions relating to
infringement of patents. In examining applications for patent, no
determination is made as to whether the invention sought to be
patented infringes any prior patent. An improvement [to an] invention
may be patentable, but it might infringe a prior unexpired patent for
the invention improved upon, if there is one."

"General Information Concerning Patents" United States Patent and
Trademark Office (January 2005)
http://www.uspto.gov/web/offices/pac/doc/general/#infringement

"A common misconception is that the patent gives its owner the right
to make, use, or sell the invention. It only gives the owner the
ability to exclude others from making, using or selling the invention.
The patent owner may be forbidden from using the invention, usually
due to the existence of another patent, or sometimes due to other
legal restrictions.

To illustrate this principle, consider the following common case:
Person 1 patents an invention. Person 2 later patents an improvement
to the invention. In order to make, use, or sell the improved
invention, one may need permission from 1 (due to the patent on the
original invention), and also permission from 2 (due to the patent on
the improvement). For example, suppose person 1's patent has a claim
covering apparatus comprising a seat and legs (a chair). Suppose
person 2's patent has a claim covering apparatus comprising a seat,
legs, and two curved rails (a rocking chair). Someone who would hope
to make apparatus comprising a seat, legs, and two curved rails will
have to get permission from both person 1 and person 2. Another choice
is to wait for person 1's patent to expire; then permission is needed
only from person 2. Still another choice is to wait for both patents
to expire."

"What is a patent?" Oppedahl & Larson LLP (June 29, 1995)
http://www.patents.com/patents.htm#whatis

Additional material you may find useful:

"What constitutes infringement of a patent?"  Nolo (2006)
http://www.nolo.com/article.cfm/ObjectID/FC5FEAF9-C546-412D-9A6852A4B981CDA8/catID/72CD4B7A-D30A-4CCF-96755FFC2292238C/310/101/198/FAQ/#0C1A03BB-CB08-41C0-831569D06A1F8CB2

"Tips on Writing Patent Claims" by Mary Bellis, About (2006)
http://inventors.about.com/library/weekly/aapatentclaimsa.htm

"Patent Claims" LegalMatch (2006)
http://www.legalmatch.com/law-library/article/patent-claims.html

"Patent Infringement" LegalMatch (2006)
http://www.legalmatch.com/law-library/article/patent-infringement.html

"Defenses to Patent Infringement" LegalMatch (2006)
http://www.legalmatch.com/law-library/article/defenses-to-patent-infringement.html

Search terms: "patent claims"; "infringes on another patent"; "patent priority"

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Request for Answer Clarification by centure7-ga on 12 Feb 2006 18:42 PST

I believe you are saying that:
A mixture of A & C, without component B is legally covered by both
John's patent and Jill's patent. Therefore, you have to have
permission from both John and Jill to manufacture such a product.
Mixture of A, B, & C is legally covered only John's patent. Therefore,
you need permission from only John to manufacture such a product.

Is that right?

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Clarification of Answer by wonko-ga on 13 Feb 2006 14:32 PST

Yes, only John's permission would be needed to make A, B, and C into
Z.  Jill could not obtain patent rights to John's existing process
with her new patent.

Sincerely,

Wonko

Answer appears well-researched.