When I was growing up, my best friend and my stepfather shared the same birthday (9/18), and my best friend’s father and I shared the same birthday (5/4). Weird.
I was conceived right when my mother’s father died. My daughter was conceived when my mother died. Neither one knew their grandchildren at all. I’m hoping that the trend doesn’t continue for me.
My husband is 10 days older than I. We’re both the youngest of four children, and each have three older sisters. We both have sisters who are seven years older, and these sisters are the closest to us in age.
My grandparents (mom’s parents) died on the exact same date one year apart. Grandfather: May 10, 2000. Grandmother: May 10, 2001.
My paternal grandmother died on what would have been the 60th anniversary of my mom’s parents.
My niece was born on her father’s 20th birthday, and my daughter was born on my niece’s 20th birthday.
My youngest daughter was born on her father’s birthday.
The biggest coincidences I’ve found, though, have to do with interactions between my husband’s ancestors and my own. [Background: Tony and I are both the products of families that have lived in a relatively small, isolated, and rural part of the southern United States for many generations. Knowing this, I did a bit of a genealogy background check before I’d even date him, because who wants to run into your own relatives at your boyfriend’s family reunion?]
As far as I can discover, we have no common relatives or ancestors in the past two centuries - which is amazing in itself, when one considers how very small the population of Georgia, south of the Altamaha River, was during all of those decades. Both of our maternal families lived for several generations in a small community that no longer exists - the landowners were bought out and all residents removed at the start of World War II, due to the expansion of Camp/Fort Stewart. Tony’s mother’s family have included a number of doctors through the years, and these were almost certainly the only doctors/dentists in such a rural town. Tony’s great-grandfather was the doctor who delivered my grandfather in 1923 and one of his three siblings. The other two were almost certainly delivered by his great-great grandfather, if there was a doctor in attendance of the births. Further back, in the 1850s, there was a very unusual name in my granddaddy’s family tree - I found the same name one generation earlier in my husband’s family tree. Apparently, the baby was named for the doctor who delivered him.
Dad’s family had babies born in
1949
1959
1969
1979
1989
Sometime in the 90s I noticed the pattern and commented on it, and that broke it. Anyway, out of 12 people, 5 were born in years ending in 9.
Recently I realised we have a trend towards wives being older than husbands (or life partners for those who aren’t married but are otherwise paired for life). My grandparents started it - Grandma was older by 3 years. My mum is six months older than my dad, my sister in law is three years older than my bro, and I am a whopping six weeks older than Div. It still counts. 
My dad’s sister’s has two kids - her son is married to a woman six months older than him, and her daughter is partnered with a man three years younger than herself. None of the rest of the cousins have paired off yet, and now that I’ve noticed the pattern and commented on it etc etc. We cougar couples are still going to outnumber the others for a while.
My birthday landed on Sunday this year as did my wedding anniversary, and the birthdays of both my children, and my wife, and my father, and both my grandfathers and three out of eight of my great grandparents. Thus the birthdays of ten of my closest relatives (eleven counting the wedding anniversary) all landed on Sunday this year. In fact, all ten land on the same day every year … except that my wife is off by one in leap years.
The odds of at least eleven out of 19 day slots being the same day are 800,000-to-1 against. (Yes, I know Littlewood’s Law 
)
Not date-related, but after my dad died, my mom brought out a bunch of old photos, including one of my paternal grandfather at work at Bethlehem Steel when he was a young man. My husband looked at the picture and immediately knew that my grandfather work on a wire galvanizing line. As it happened, my husband’s first engineering job was designing and installing a wire galvanizing line. And on top of that, my mother gave us my grandfather’s wedding ring, which Dad had kept - my husband wears it now since his original ring was damaged.
I don’t remember a lot about that grandfather because he hardly spoke English and I was just 10 when he died, but I like having the connection.
I’ve had two mothers-in-law with the same maiden surname, a fairly uncommon name that ranks just barely in the top 1,000 most common names. They were unknown and probably unrelated to each other, although both had roots in widely separated parts of Canada.
Ive had two nieces and an aunt who married men whose names were all different, but on the same page in a large city phone book.
The first time my wife met my father, he was exactly twice her age, to the day. (One day before her 46th birthday, two days before his 92nd.)
I visited my grandparents when I was 27 and was told:
“my mother had me when she was 27, I had your mother when I was 27, your mother had you when she was 27. You have two months to make a baby”.
I figured I’d rather break the trend.
My birthday is exactly equidistant between my parents’ birthdays - December 26, January 16, February 6.
I also share my birthday with my grandmother’s youngest siblings (a pair of twins).
OH…and both my parents have brothers names John and Peter.
My husband’s parents and my parents share a wedding day. I was born four years and six months later while DH was born seven months later. His mother tried to hide the year of her wedding from me but I’ve seen her wedding certificate. Heh.
My brother and I were born exactly 1 1/2 years apart, him on November 14, 1965 and me on May 14, 1967.
By the time my parents were married, my paternal grandfather had died, and my maternal grandmother had died. So my maternal grandfather married my paternal grandmother. They were the only grandparents I knew, from both sides. This made my parents step-siblings, after they were married.
My paternal grandmother and her twin sister married two twin brothers (their first husbands).
My brother was born late on September 30, and I was born early on October 1 (nine months after New Year’s), three years later. My mother finally admitted that the only way my father would get her pregnant was to get a few drinks into him. And since he rarely drank, that was easiest to do on New Year’s Eve.
My first cousins’ ages have a range of over 40 years.
My partner and I share the same birthday, 20 years apart.
Both my kids were born on a Wednesday, on the 28th of the month, six years apart.
Yesterday, at the tender young age of 64, I suddenly realized that my two grandfathers’ names were Bert and Ernie.
My inlaws (father, mother and brother) are buried together. My BIL died on my wife’s birthday and my MIL on mine. So our birthdays are date-of-death on the same tombstone. That strikes me as fairly odd.
Not in my immediate family (I think third cousin or so), but:
A family of five children, two daughters and three sons. The mother, one of the daughters, and all three daughters-in-law are named Mary or some variant thereof (Maryann, Mary Jo, Mary Beth, etc). The one female that isn’t named Mary comes really close (May or Myra or Amy or something).
(from OP)
If your family gave us Miley Cyrus or Snooki, I am going to be very upset. I unfortunately was born on 11/23 also, and recently made the mistake of telling a coworker about this.
My coworker’s reaction: (laughing) “Dude, that’s awesome!” My reaction: “What are you, nuts?”
While vacationing, my grandparents received two telegrams, from two different kids announcing the birth of their second grandson.
In other words, a cousin and I were born on the same day, just a few hours apart.
I’ve posted this before but my niece was born on 12/12/12 at 12:14 PM. I was born on October 11th so that year my birthday was on 10/11/12.