Are there specific guidelines, rules, or United States law that
determine how research data is to be collected in order to be
considered scientific and valid for acceptance by the scientific and
medical community? If these exist, what are they?

Hello Road,

There are a great many guidelines and laws applying to collection of
research data.  I have included five major categories in my answer,
but there may be more that apply to your specific situation.  Please
request clarification and provide more specifics if your question is
not answered here.

University/Institution Guidelines

If you are conducting research as a student at a university or through
an institution such as a hospital, in all likelihood there are
institution-specific research guidelines and rules.  Check with your
academic advisor or department before beginning your research.

Here is an example of one university?s guidelines, from Harvard:
http://www.fas.harvard.edu/%7Eresearch/greybook/toc.html

Funding Guidelines

If you plan to apply for funding for your research, you may find that
there are guidelines or rules governing the particular grant you are
seeking.  Check with any grant-making institutions you may want to
work with prior to beginning your research.

Peer Review

All serious scientific research is at some point subject to peer review.  

According to the UCLA Sponsored Research Glossary, Peer Review is defined as:
?A system using reviewers who are the professional equals of the
principal investigator or program director who is to be responsible
for directing or conducting the proposed project. It is a form of
objective review. Peer review is legislatively mandated in some
programs and in other programs is administratively required.?
http://www.research.ucla.edu/sr2/gloss.htm#p

Basically, peer review is the system through which colleagues
objectively evaluate each other?s work.  Work is submitted in the form
of a paper, which is reviewed by a panel of colleagues for scientific
merit and accuracy.  Where peer review is part of a grant application
process, a scholarly work may also be ranked according to
grant-worthiness.

In a sense, the work that has already been done in your subject area
is the most important guideline to keep in mind.  A thorough review of
those peer-reviewed articles already published in scholarly journals
will give you an idea of what is considered acceptable in your
discipline.

Research on Animals

Research on animals is subject to specific laws and guidelines, such
as the Health Research Extension Act of 1985 and guidelines from the
Public Health Service of the NIH.
http://grants.nih.gov/grants/olaw/references/phspol.htm
The focus of these laws is on reducing distress through appropriate
use of anesthesia and other methods, and providing appropriate
veterinary care.  The animals must also be cared for humanely
according to the Animal Welfare Act.

Research on Human Subjects

In part from the fall out of the infamous Tuskegee experiment (in
which African American men went untreated for syphilis for 30+ years
after a cure became available)  congress passed the National Research
Act in 1974.  Since then many rules and guidelines relating to
research on human subjects have been promulgated.  In addition to
federal laws and the NIH guidelines, most institutions have their own
guidelines on the subject which should be strictly adhered to.

National Institutes of Health Office of Human Subjects Research
http://www.nihtraining.com/ohsrsite/

Guidelines facing academics doing research on human subjects:
http://www.fas.harvard.edu/~research/HumSub.html
*note that some of these are specific to Harvard and some apply more generally

From the Code of Federal Regulations, Protection of Human Subjects:
http://www.fas.harvard.edu/%7Eresearch/45CFR46.html 

I hope this is the information you were seeking.  If you have more
specific needs you would like me to research please request
clarification before rating this answer and I will be happy to help.

Regards,

Majortom

Thorough, concise, had all the answers I was looking for.