Provided you qualify for home, non-commercial use and they are in the same home, yes you can use the same avast 4 home registration key.

http://www.avast.com/eng/faq-registration-license.html#idt_6920

Q: I have “avast! 4 Home” installed on my home computers and have entered the same license key on all of them. Does using the same license key on more than one computer harm the avast! functionality or updating capabilities in any way?

A: No, it doesn’t. The registration of “avast! 4 Home” is implemented due to processing statistics. The same license key on more computers (provided they are used for non-commercial purposes and in home use only) doesn’t harm the avast! functionality or ability to update in any way.