At the risk of generating more traffic and giving him a better PageRank, I’d like to point you to a website spreading general mis-information:
I would have simply sent them an email, or posted on their ‘blog’ but sadly there is not such facilities provided at the aformentioned link. It irritates me because this is being posted on a site which claims to have medical information.

This article is linked from a post on a web-forum made by someone who lists themselves anonymously, and I’ve seen it elsewhere on other sites as well. However, as always, I digress.

Most of this article is made up of speculation, unreferenced studies and opinions stated as facts. Further research into this also finds not one solid reference to the source of apparent Soviet testing in the 1970’s. It claims to be refering to this mysterious document which nobody can find:
Prepared By: William P. Kopp
A. R. E. C. Research Operations TO61-7R10/10-77F05

Furthermore it’s been flagged on at least one site as false:

Microwave ovens came out in the late 1940’s and have been in widespread use since the 1970’s – according to this document we should all be dead, ill or dying.
The article’s claim that microwaves cause foods to produce carcinogens is the only portion I found to be credible, but what they fail to indicate is that most foods, when cooked (regardless of how) can produce small levels of carcinogenic chemicals – and that the end effect of cooking at high-heat from a convection oven is actually more likely to do so than a microwave.

More digging finds that the few references that are to something in existance (such as the dangers of microwave radation on humans) are refering to something on a large scale passing the radiation directly through a person at high-wattage, and having very little to with what is boucing around inside your oven.

The article eventually goes off into the world of fantasy – refering to reduction of vital energy fields and nucleoproteins in foods. The first is spiritual speculation (hardly likely to be in a Soviet research document) and the second is refering to components of DNA.

Finally the summary at the bottom makes several bold statements not previously addressed in the article, and regardless – it’s all fiction anyways. It astounds me how much this article has spread and people post it like the truth.

*Update July 8th, 2010:* It appears the site has fleshed out the article a little more since this was posted, however it still does not address the damage caused to food by heating in other forms compared to being heated by a microwave so I still consider it unnecessary fear mongering.