e.g.
(1) Your Moon is the same sign as one or more of your father/mother's Sun, Moon, ASC/DESC/MC/IC/Mercury/Venus/Mars/Jupiter or Saturn
My mother is a Capricorn sun, moon, and Saturn. I am a Capricorn moon. Her Saturn is conjunct my moon.
Not comfortable at all, for either of us.
My middle brother is a Cancer sun; my mother is a Cancer ascendant and my father was a Cancer moon.
In my own family, both of my children are Virgo moons and I am a Virgo sun.
In my husband's family, he is a Pisces moon and his mother and our daughter are both Pisces suns.
My FIL's Pisces Saturn also sits on my husband's moon.
(2) Your Sun is the same sign as one or more of your father/mother's Sun, Moon ASC/DESC/MC/IC/Mercury/Venus/Mars/Jupiter/Saturn
Mine isn't, but my husband and son are both Aries suns.
My father was born August 23,
but by birth time and location was a Leo (August 23 is one of the most tricksy birthdays astrologically, it seems).
He had Venus and Mercury conjunct in Virgo.
I am a Virgo sun, born August 27, and have Venus and Merc in loose conjunction in Leo.
I always thought that was interesting.
My oldest brother is a Virgo moon.
(3) Your Ascendant is the same sign as one or more of your father/mother's Sun, Moon ASC/DESC/MC/IC/Mercury/Venus/Mars/Jupiter/Saturn
Hahahaha, yes.
My dad and I were both Leo rising.
My son is also Leo rising. They are all placed no more than two degrees apart from each other.
(I laughed because my son was a preemie
and my mother had everything but the time keyed in to the computer when the date was determined
-- I had severe preeclampsia and he was delivered by emergency c-section.
When she did the chart and told me he was a 10 deg. Leo rising to my eight, I cracked up, and that laughter was much appreciated!)
Basically - is one of more of your ASC/DESC/IC/MC/Moon/Sun/Mercury/Venus/Mars/Jupiter/Saturn the same sign as one or more of your father/mother's ASC/DESC/MC/IC/Mercury/Venus/Mars/Jupiter/Saturn signs? 
Just a tad, especially with me.
My two older brothers brought completely different signs to the astrological gene pool.
I am the most tied, astrologically, to our parents -- and, paradoxically, was always the most rebellious.
One interesting thing about the three of us, at least to me: my eldest brother has no water in his chart.
My middle brother has no earth.
I have no air.
I wonder if Mom and Dad had had a fourth, s/he would have had no fire? 
We all have Venus and Mercury conjunct -- in different signs,
but nonetheless we share that aspect with our father, who also had it.
(An interesting tidbit: I am 13 and 11 years younger than my brothers.)
... and after I read through this I got the impression that JUPITERASC is interested in gathering info about this subject,
so I have more to add regarding my kids, in-laws, nieces and nephews (I promise not to write War and Peace, lol).
Taurus:
My oldest brother, by all appearances, introduced Taurus to our DNA.
It does not exist in either of our parents' charts nor, as far as I can tell, does it go farther back
(but one starts to run into difficulties with birth time and such then, so it's hard to tell).
My bro is a Taurus sun/ascendant.
There are six bio. grandchildren (two more adopted) on my side of the family.
One nephew and my daughter are both Taurus rising (and they're 19 years apart; he's the oldest grandchild, she's the youngest).
A niece (who is also my godchild) has her moon in Taurus.
My son has Venus and Mercury conjunct in Taurus.
Scorpio:
My kids' generation brought Scorpio to the family.
Two of my nieces are Scorpio suns
(in fact, the one with the Taurus moon is also a Scorp sun, and they oppose each other).
My daughter has Mars in Scorpio (and can you ever tell; that is NOT a criticism).
All three girls, despite having three different sets of parents and quite an age spread, are very much alike temperamentally.
The eldest niece also picked up that Capricorn moon from my mother.
Aquarius: My middle brother is an Aquarius moon. My nephew -- son of my other brother -- is an Aquarius sun AND moon.
We're a Fixed lot, aren't we?
My husband's side:
MIL, Pisces sun/Sag moon. (I don't know her birth time, so I have to do a 12 noon chart for her.
I don't dare ask; it wouldn't be prudent.)
Her own mother was also a Pisces sun; one of my husband's cousins shares his grandmother's birthday.
My MIL has Venus in Aries, as do my husband and daughter.
She also shares a Saturn in Aries placement with my son and a Jupiter in Aries placement with my daughter.
Hmm. Three of her six grandchildren are Pisces suns (my daughter, one niece, and one nephew).
Two are Aries suns (my son and another nephew).
No Sag there that I know of, but again I can't ask that side of the family what their birth times are and why I want them.
FIL, Scorpio sun/Capricorn moon. One Scorpio granddaughter.
His Pisces Saturn sits on my husband's moon.
He has absolutely nothing in common with either of my children astrologically,
unless his unknown ascendant would change that.
He and I have a lot of conjunctions and/or oppositions (including Saturn), which I find interesting since I married into the family.
Again here, my husband is the youngest and the one with the strongest astrological ties (in his case, to his mother).
His sister is a Cancer sun and his brother's an Aquarius sun;
I don't know the rest of their astrology but I know there's a pattern of detachment in that family and I wonder if I did everyone's chart
(even with a 12 noon) if I'd find Venus in Aries or a lot of Sag moons.
Since it's supposed to rain all day I know what I'll likely be doing if I get bored.
