Until Google adds this feature to Google Calendar, you can try a third-party application that generates a public calendar for the birthdays associated with your contacts. The application uses Google App Engine and Google Contacts API, so your password is safe. Another good thing is that the calendar is updated automatically when you add new birthdays or you edit the existing ones. Add notifications if you want to receive an email or an SMS one day before each birthday.
The major downside is that the calendar generated by the service is public, so anyone who knows its URL can see it. To use the service, you need to grant it access to your address book and Google recommends to do only if you trust the site. It's always a good idea to export your Gmail contacts before using an application that is allowed to has write access to your data.
Update: Google Calendar added the same feature. Go to the Settings page, select the Calendars tab and click on "Browse public calendars", then add the calendar "Contacts' birthdays and events". Unfortunately, Google's built-in calendar doesn't support notifications.
For some of your contacts, you'll see their birthdate even if you didn't add it to Google Contacts. It's likely that the information is obtained from Google Profiles.
{ Thanks, WebSonic.nl. }