There has been a lot of talk about BLUE-GREEN ALGAE, and a great deal of confusion about what it really consists of, what the various health benefits might be, and what harm it might do. Further complicating the issue is the fact that there are several things which are called "blue-green algae"; Most of them are actually cyanobacteria, which are actually bacteria and not algae. The other things are spirulina and chlorella, both of which are single-celled algaes, and are actually green, not blue-green. Spirulina is used as a nutrient supplement, but it provides nothing that cannot be had elsewhere more efficiently. Chlorella has some interesting properties, especially in the area of blocking various viruses and toxins.
However, only 30-50% of cyanobacteria is nontoxic. Some cyanobacteria, AKA pond scum, generate a number of toxins which are irritating or even deadly. Cyanobacteria can product hepatoxins, which affect the liver, neurotoxins, which affect the nervous system, or various other chemicals which will cause rashes of the skin and mucous membranes. None of these byproducts are likely to kill you, but they are all dangerous. They can cause headaches, fever, diarrhoea, abdominal pain, nausea and vomiting. They are dangerous to both people and animals, and because the danger is from the toxins and not from the bacteria itself, boiling the water (or the bacteria) does not make it safe.
Ultimately the health effects of chlorella have yet to be scientifically determined, though the results are so far encouraging. Spirulina would appear to be purely a gimmick. And finally, the actual blue-green in our algal spotlight is not actually algae, but generally toxic cyanobacteria which are usually harmful, and repeated exposure to which could ultimately be fatal, and will almost certainly cause long-term health issues.
Webpage: Health Canada, BLUE-GREEN ALGAE (CYANOBACTERIA) and their toxins (http://www.hc-sc.gc.ca/ehp/ehd/catalogue/general/iyh/algea.htm)
Webpage: Quackwatch, Algae: False Claims and Hype (http://www.quackwatch.com/01QuackeryRelatedTopics/algae.html)
Webpage: ZetaTalk, Chlorella (http://www.zetatalk.com/food/tfood27t.htm)