I'm aware of the fact that the standard contacts/calendar app does not support birthdates synchronization (Android issue 1211). But may be there is some third-party software which can make those synchronized for me?
Is this still a problem? I see birthdays from contacts in Calendar.
I add birthdays to my contacts in Gmail, and I subscribed to the "Contacts' birthdays and events" in Google Calendar:
This gives me a calendar in Google Calendar with my contact's birthdays.
When I got my android (a motorola xt720 running eclair), the birthday calendar showed in the Calendar app.
You'll probably have to open the Calendar app > Menu > My Calendars. And then Menu > Add calendars. You should see Contacts' birthdays and events.
gCalBirthdays is what you're looking for. It comes as a Google Calendar Sidebar Gadget and reads your contacts birthdays in one of your Google calendars which you can then sync to your android phone.