I've been updating the full list of birthday freebies regularly, as it's still an insanely popular page on the site, and I'm happy to say I finally was able to confirm the Starbucks birthday freebie of a free handcrafted beverage or food item!
In order to get this, you have to join their loyalty program. You'll receive an email around your birthday informing you that you can choose from a free handcrafted beverage or free food item. The coupon will be loaded onto your account.
The full terms of their program are long, but tl:dr, is that you get to choose between a free drink or snack. You much join their Rewards program at least 7 days before your birthday and you have to make at least 1 Star-earning transaction on your account. The birthday reward should be added to your account 2 days before your birthday.
Also, for the record, I want no hands actually touching my free handcrafted beverage, please.