I share the same birthday with one of my school friends or as my father would have said 'one of my oldest living friends'. We've co-hosted the odd party but generally, we tend to do our own thing because we live in different parts of the country.
We used to buy each other birthday presents (nothing major - a novel or such) but then it might take us up to 6 months to meet and exchange. About five years ago, we went to a play during the Dublin Theatre Festival and decided there and then that this would be our present. We would go a show during the festival every year, we go Dutch on the tickets because it's not about who pays or not - the point is that every year we make an effort to do this together.
In five years, we've never missed a show and we tend to get in touch more in the months leading up to the festival to decide on the show before it sells out. It's a far nicer way to mark our birthday - presence not presents - and an outing I look forward to every year. You might not be into theatre but try it for something else - a movie, a gallery outing, a hike, a swim in a fjord - whatever floats your boat. Why not send this Happy Birthday card to seal the deal?