Starting from Magento 1.9 the order confirmation emails are not sent during checkout anymore, instead they are sent with the Cron. To verify this works properly:
make sure your system Cron is up and running (you can check the Cron logs: /var/log/cron to verify that).
make sure Magento Cron is setup correctly and is running every some minutes. You should see something like this in the Crontab of your system:
*/5 * * * * /public_html/cron.sh
This schedules a task to run cron.sh every five minute. (More reading)
There are good extensions like AOE Scheduler in Magento that help you to monitor and manage Cron jobs.
To debug magento order mail issue regarding new order just run yoursite.com/cron.php If you recieve any mail now then its cron issue. You can fix con issue by setting cron in cpanel.