Update: Google Calendar has added the ability to add your contacts’ birthdays and other important dates to your google calendar! 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.