Earlier quoted context omitted.
In the US, President Bush signed the Genetic Information Nondiscrimination Act of 2008 which covers these topics. Some relevant parts are available here: http://thomas.loc.gov/cgi-bin/bdquery/z?d110:HR00493 : edit: Specifically, "`(A) IN GENERAL- For purposes of this section, a group health plan, and a health insurance issuer offering group health insurance coverage in connection with a group health plan, may not adj…
Note that it doesn't prevent discrimination for life insurance, disability insurance or long-term care insurance; if you get a dangerous condition in your DNA testing you'll never get any of those types of insurance again. Also note the limitations are not very comprehensive. Health insurers could use genetic info and then find ways to deny you coverage on a technicality (didn't disclose tonsilitis at age 4 - DENIED)…
How could that work once the Affordable Care Act goes into effect? It requires Guaranteed Issue, so insurers can't do that. Insurers have to accept anyone who requests their plan and they can only vary premiums based on age, location, and smoking.