The search function and the internet have taken some of the fun out of finding the answers to questions like these. As noted, the addition of iodide to table salt appears to have been a public health type action. As for the iodide pills doled out near nuclear plants and other potential exposure situations, I think one of the common by-products of nuclear reactions (and that would be present in a
release) is a radioactive isotope of iodine that can be readily taken up by the body (or maybe just the thyroid gland). Taking the iodine tablets "saturates" (so to speak) the human body with iodine so that the radioactive iodine is not adsorbed, thus reducing exposure to radioactivity from that particular source. However, the tablets do not afford any other general protection from radioactivity or other radioactive isotopes.
I think that fluoride is the only additive in the US drinking water as a part of an overall public health program. However, there are some US public water suppliers that still refuse to fluoridate. There is a great deal of controversy on the subject; I've never investigated the health issues of fluoridation much further although plenty of documentation can be found. (And the subject always reminds me of the General Ripper character in Dr. Strangelove.)
On the other
hand, chlorination isn't all its cracked up to be. Great disinfectant, but chlorine reacts with the miscellaneous organic material in water (particularly found in surface water sources) to generate a number of hazardous disinfection byproducts (DBPs). For more information, see:
http://www.epa.gov/safewater/mdbp/dbp1.html
Joe