I believe email notification when there is new order is an important feature. However, it's weird that Magento does not support this feature. Luckily, there are some ways to make this happen and in this tutorial, you can find out 2 answers.
Here we go:
1) Install a custom module
There are some free modules which can do this. Searching from Magento Connect is help. But it can cost you some bucks. In case you want something free, you should try the 2nd option. I am thinking of having one free for this simple thing, will update here when it's available.
2) Configure from admin panel
Go to System > Configuration > Sales > Sales Emails. Open Order tab, enter your email in field "Send Order Email Copy To". You can add more than one email by comma separating.
You can also receive this email as BCC or a separate email, so there is no worries that customers will know that.