How can I test my drinking water inexpensively and reliably for contaminants? 
Are home test kits the way to go?  Do local municipalities do this
for free or for a nominal fee?

Hello pcventures and thank you for your question.

Depending on what type of contaminants you are looking for the
Environmental Laboratory of Westchester County can help:
http://www.westchestergov.com/labsresearch/publichealth/environlab/environlab.htm

The fees vary from five dollars to hundreds, but the accuracy of the
results will be greater than those from a home testing kit:

Schedule of fees:
http://www.westchestergov.com/labsresearch/publichealth/environlab/fees/2003fee.pdf

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Westchester County also provides some useful information on water
quality:
http://www.westchestergov.com/waterquality/

For more infromation regarding drinking water quality see:
http://www.epa.gov/safewater/dwinfo.htm

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A home water quality testing kit that you can buy online is the:
 
"WS-425B
WatersafeŽ All-In-One
Comprehensive test that checks for Bacteria, Lead, Pesticides,
Nitrates, Nitrites, Chlorine, pH and Hardness"
http://www.watersafetestkits.com/pages/products.html

It costs $16.99 and you can order it here:
http://watersafetestkits.com/shop/enter.html

Thank you for your question and if you need any clarification of my
answer, do not hesitate to ask.

Very best regards

THX1138

Search strategy included:
"home test kit"  "water quality"
://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&safe=off&as_qdr=all&q=+%22home+test+kit%22++%22water+quality%22

Great answer.  Thank you for your help.