It makes you wonder if people are bad at statistics.
3 older sisters, them me - a “rhythm” accident! 
All your older sisters were born before you?
My mother gave birth to a son (me) then another son, my brother, sired by two different men.
My father sired a son (me) then a daughter, my sister, borne by two different women.
Among my siblings: son, son, son, son, daughter, son
My brother’s kids:
son, son, son, son (the last 3 they were trying for a girl)
son, son
daughter
I have one child, so I voted based on my own sibling situation.
As an aside, my mother has seven siblings, and each of them (save one, who has no children) has two children. Interestingly enough, each of those are matched sets, and there are 3 sets of each.
In order:
2 boys
2 boys
2 girls
2 girls
2 girls
2 boys
2 daughters for my kids
2 sons for my parents
1 son 1 daughter for my oldest daughter, and one son so far for my youngest.
2 sons, 1 daughter for my father’s family
4 daughters for my mothers. Then my grandfather gave up trying to get a son.
I don’t know any daughter/son families, so that means my anecdote cancels Velocity’s.
I’ve been interested in this question but for another reason. Many people believe that some people - and in particular some women - are predisposed to give birth to more children of one particular gender. (Theories I can recall - from those of a scientific bent - have mostly involved the acid level in the vagina, which is apparently more hospitable to one or another type of gene.)
But it’s very difficult to assess this type of claim, since even by pure chance there will be some people who will have overwhelming majorities of children of one gender. For example, if you look at families with 4 children, one of every 8 will have all 4 of the same gender just by pure chance. Some it will seem as if these people are predisposed to one gender when really it’s just random chance.
So I think the simplest way to assess the validity of the notion is by looking at the first two children of many families, and comparing the number which have both of the same gender vs those with one of each gender. If some people are predisposed to have a particular gender, then the percentage of those with the same gender would be over 50%. If it’s purely random, then it should be a 50%/50% blend. From looking at as many people as I could find, I didn’t find any indication that same-genders were above 50%. But perhaps I didn’t look at enough couples.
Seems an appropriate thread for this anecdote: I have 2 sons (and we don’t plan to have more children). My father had only 2 sons. His father had only 2 sons. And his father also had only 2 sons (twins in this case). Combined with longish generation gaps, this has led to no females in this branch of the family tree since the mid-1800s. But among the billions of families on earth, even this is not so remarkable.
Reflecting on this, it’s a non-trivial question what distribution we should expect under the null hypothesis that births are independent with ~50% probability. Under this model, nothing you can do will change the probability of the sex of your next child. But you can, of course, control the size of your family. And some parents appear to be motivated to keep having kids until they get one of the particular sex they want, or until they get one of each. So even under the null hypothesis we might expect large families with initial runs of one sex to be overrepresented, i.e. the following distributions:
BBB
BBBB
BBBBB
BBBBBB
(kept trying for a girl, eventually gave up)
BBG
BBBG
BBBBG
BBBBBG
(kept trying for a girl until they succeeded)
and the converse with G/B flipped
I wasn’t sure if I should go my family counting me as a child (i’m second of 4 girls) or to count my family as in my children (BBGB).
At least 70% of my coworkers are oldest children. And because the majority are also women, they’re mostly oldest daughters. I know way more people who are the older sister of a younger brother next than any other combination.