I went to elementary school with a boy who was born the same day as me. I can’t recall who was the older of the two… the difference was only a handful of hours, though, IIRC.
Back when I was in the throes of a mad schoolgirl crush over said boy, I of course took this as a sign that we were Meant To Be… it wore off after a month or so. 
I have met two people born on the exact same day as me in real life. One was a high school classmate who born in Iran so she might have been born on a different day if we account for time zones. One was a friend of a friend. I only met her a couple of times but since I was born after 11pm, I had much fun teasing her that she was the oldest.
Back in the late 90’s when we were all getting those disks for a free hours of AOL in the mail, I would sign up from time to time until the free account ran out. Once I did it on my birthday and did a search for anyone on-line who had the exact same birth date. As I recall, there were seven or eight of them. I IM’ed and chatted with a few of them.
A girl in my grade and I were born on the same day in the same hospital. She was a few hours older than me. My husband is 10 days older than me.
A friend whom I’ve known since school. We were born on the same day. He’s a couple of hours older.
I have a cousin who is eight days younger.
When I was in grad school 3 of us in the group I hung out with had birthdays within 3 days of each other - same year.
Prince Charles and I share a birthday, but different years.
Going off on a tangent here but I spent grades 2-12 with the girl who was born on the exact same day as me.
Our personalities were completely different and various thing in our lives (tragedies, romance, fortune, etc.) never seemed to coincide.
It was over these 10 years together that I concluded horoscopes were complete b.s.
There were five people in my graduating class who had the same birthday as me, including me and my twin. I don’t know what time they were born, though.
Damnit. After my twin, I can’t really think of anyone with a b-day close to mine. I seem to remember someone having my b-day but not the same year, which isn’t exactly the spirit of this thread.
The closest I can say for myself was a friend I had in high school who was two days older.
However, my mom’s best friend and her husband were both born in the same hospital less than an hour apart, IIRC.
The Bush twins are one day older than me. I found a long list of “celebrities” that were born on the same day as I, but never heard of any of them.
Oh! Tina Turner…and Charles Schultz…but many many years before.
My first year in college, there was a guy on my floor in the dorm who had the exact same birth date as me. We were both English majors, and we weren’t dissimilar looking (except that I’m Latino and he was Japanese). We got along great, but he moved to a house the following year and we grew apart after that. Always wondered what happened to him…
My best friend in elementary school and junior high was 5 days older than me. I don’t recall ever meeting anyone else who is as close to my birthday as that.
When I was in the Army I met, and became roommates and good friends with a guy who was born in the same hospital as me, within about the same week as me. We always joked we could have been switched at birth, and have the wrong parents.
I also dated a guy born I think two or three days before or after me, but he was from the south.
When there was a birthday thread on the SDMB another poster, twickster, and I, discovered that not only did we share the same birthday, but the date as well. twickster is likely some hours older than me, as I was born at 10:16 PM.
The niece of one of my family friends is ten days older than me. We got along quite well in our early teen years, and I haven’t heard much from her since. Living across the Atlantic Ocean from each other and never having time to visit does that to relationships, but I hear semi-regular updates from her aunt via my mom.
There is a girl I know at church who was born on the same day as me. She’s not someone I know from childhood or anything (neither of us are from Chicago) so we didn’t figure this out until last year when I invited her out for my 30th birthday. She couldn’t make it because, well, it was her 30th birthday.
She has family plans again this year (birthdays happens to be tomorrow). I am authorized to accept drinks on her behalf.
I had several college classmates who shared my birthdate, but we never bothered to discuss actual time of day. I don’t kow mine, anyway.
Nicole Richie and I were born on the same day, same year. One of my good friends was born same day, the year before.
I have a cousin who is a half hour younger than me.