There is a lot of false information, such as looking at cron jobs, inside this thread. Most of you likely have different causes but the same result for this 'issue'.
I will try to summarize what can cause this issue, and what you can do to resolve and debug it.
POSSIBLE CAUSES OF NO ADMIN EMAIL
1) SETTINGS > EMAIL > NEW ORDER > Recipient(s) field misconfigured - this field can override the 'admin email address' setting of WP to control whom gets emails.
2) Email going to spam-box. HTML emails especially can go to spam. The email settings section will let you choose 'plain text' instead of 'html' if you wish to reduce the likelihood of this. *or* find what is blocking the email and whitelist woo emails.
3) Settings > Emails > Email 'from' field. Some server environments refuse to sent email from anyone but a certain email domain. Clear these fields or set to a domain which is allowed (check with the host). I believe some godaddy setups have this limitation.
4) Bad template override in theme. Switch to the 'twenty eleven' theme and repeat. If it comes through it may be an override (overrides are listed in WC > System Status for you, and if the email templates are overriden and causing issues contact the theme author - FYI they should not override all templates!).
5) Plugin conflict. Turn off all plugins bar woocommerce to test.
6) Finally, check to ensure orders are not 'pending' and are indeed going to 'processing' or 'complete' status. Pending = unpaid. If you are using paypal and orders are pending, but you know they have been paid, you have an paypal IPN issue. http://docs.woothemes.com/document/paypal-standard/#section-6
IF ALL ELSE FAILS the host may be responsible. Trying SMTP plugins may help but at the end of the day the emails are being sent via your server - contact the hosting provider and ask for assistance.