The US are behind the curve on this ;-).
Norway Extends Compulsory Military Service to Women
100 years after Norway introduced full voting rights for women, the Norwegian Parliament voted to adopt compulsory conscription for women as well as men with an overwhelming majority.
Why did they do it?
This does not mean that all women must serve in the military. Women will, however, be subject to conscription on an equal basis with men, making them as likely to serve in the military as people of the opposite gender. Norways armed forces have an annual requirement for 8-10.000 conscripts out of a total of 60.000 men and women in the relevant age group. Recruitment is already high and increasing, and the number of applicants each year exceeds the needs of the Armed Forces.

• We do not adopt conscription for women because we need more soldiers, but because we need the best, no matter who they may be, says the Defence Minister, and adds: - High-tech equipment alone does not make for a modern military; we also need a modern and diverse organisation with different people, skills and perspectives.
  Quotes from the website of the Norwegian Embassy in the UK:
  http://www.norway.org.uk/norwayandcountry/current-affairs/norwegian-politics/norway-extends-compulsory-military-service-to-women/
  "I only watch box sets. Soya latte anyone?" (GuardianOnline reader CameronYJ)

As much as I hate the draft/Selective Service, I think if our country is going to have it then all citizens should register. But of course there should be a bunch of criteria to consider for each individual: overall physical health, moral character, etc.