My sister and I share the same birthday, three years apart. I'm also due with this one only a few days after dd's birthday, so it's a real possibility that they'll share, too.
Sharing a birthday is fun in a lot of ways. It's very unusual, which as a kid is fun. My sister and I still get a laugh out of it sometimes. I think it's also made us closer in some ways, and as adults it's very sweet to call each other that day and exchange the "Happy birthday!" "Happy birthday!".

As kids my parents always tried to give us two different birthday parties, two different cakes, and that REALLY helped. I was sometimes a little pouty that my sis got to celebrate on the "real" birthday, but again...my parents just made us flip every year with who got the birthday party closest to the date. And once I started having slumber parties, and that kind of thing, it didn't really matter.
As teenagers she started doing the shared cake thing, and that stank. I know I probably shouldn't have cared as a teenager, but I did. It made it feel much more ho-hum. I will say though that having two birthdays on one day in a family makes that one day feel VERY special...and that was sweet.