Asus will not provide you with a serial key. However, they can provide you with your recovery media. This typically costs between $10-50 and will contain your windows operating system that came with your computer, as well as any drivers/software that came installed on your laptop when you purchased it.
The other user recommended Magical Jellybean keyfinder. I will tell you that I work for an IT company that does computer rebuilds daily, and I prefer Produkey Finder from Nirsoft. It is a very streamlined and superfast app. You can find it at: http://www.nirsoft.net/utils/product_cd_key_viewer.html
If your hard drive has crashed or you cannot boot into your OS for some reason, this may not be a viable option. If that is the case, I recommend ordering your CD from Asus. If you need to be back up immediatley, you can download your version of windows from this forum: http://www.digital-kaos.co.uk/forums/f94/original-untouched-windows-7-sp1-iso-32-bit-64-bit-220877/
You will need to activate within 30 days, but you can install and then activate once you get your CD with the correct serial number.