Google Contacts has a Birthday field but it doesn't translate to Android really and there is certainly no real way to be notified or reminded of your contact's birthdays as part of the stock user interface.
I recently found this app called Birthdays. The app automatically reads all the birthdays from your Google Contacts and organizes them is an easy to view list. You can also set multiple reminders for upcoming birthdays. In a Facebook world I like to call my friends the day before their birthday and this app can be set to remind you as many days before as you would like.
It can also be setup to integrate with different types of calendars. The app also features a variety of different size widgets that you can use. I personally don't take advantage of them but hey you might love a birthday widget on your screen.
The app is free so check it out.