Google recently announced the very sad news that they were suspending the free version Google Apps for businesses. Here are some alternatives:
Using domains.live.com you can map your domain and get up to 500 free email addresses.
If you are an educational institution of US based Non-profit you can still get Google Apps for free
Google App Engine still requires Google Apps to map domains. They’ve still kept a free version with which you can get a single account. You can probably still use multiple email addresses using catch-alls or with Google App’s “groups” feature, enabling anybody on the internet to post. You can sign up for that at the following link, but they check that your referrer is https://appengine.google.com