Do the teachers have any family (like husband, children and wife), or are they sacrificing their personal lives for the service of the school?
I have detailed canon information on a handful of professors, but I’m not aware of information about other professors except parents.
Spoilers for Deathly Hallows and Pottermore throughout.
In an extract from Rita Skeeter’s book, there’s a family photograph which shows all of the known family members of Dumbledore:
He turned a page loudly, and Dumbledore’s name leapt out at him. It was a moment or two before he took in the meaning of the photograph, which showed a family group. Beneath the photograph were the words: The Dumbledore family, left to right: Albus; Percival, holding newborn Ariana; Kendra; and Aberforth.
— Deathly Hallows, chapter 11, The Bribe
Percival and Kendra were his parents; Ariana and Aberforth were his siblings. As we learn in Deathly Hallows, the only member of his immediate family to remain alive by the time he took up a post at Hogwarts was his brother, Aberforth.
As far as we know, the closest Dumbledore came to a partner was Grindelwald. From an interview with JK Rowling:
Did Dumbledore, who believed in the prevailing power of love, ever fall in love himself?
My truthful answer to you... I always thought of Dumbledore as gay. Dumbledore fell in love with Grindelwald, and that that added to his horror when Grindelwald showed himself to be what he was.
It’s implied that this betrayal at a fairly young age rebuffed Dumbledore sufficiently much that he never had another partner. At least, I don’t know of any canon information about such a person.
Parents. Quoting from Pottermore:
Minerva McGonagall was the first child, and only daughter, of a Scottish Presbyterian minister and a Hogwarts-educated witch. […] Minerva's father, the Reverend Robert McGonagall, had become captivated by the high-spirited Isobel Ross, who lived in the same village.
Isobel kept her magic a secret from Robert for a long time, after they were married and after Minerva’s birth. When she finally revealed her magic, the secrecy shook their relationship, and this had a lasting effect on Minerva.
Brothers. Again, from Pottermore:
Two more children, both sons, were born to the McGonagalls, and both, in due course, revealed magical ability. Minerva helped her mother explain to Malcolm and Robert Junior that they must not flaunt their magic, and aided her mother in concealing from their father the accidents and embarrassments their magic sometimes caused.
Fiancée. After leaving Hogwarts, she fell in love with the son of a Muggle farmer, called Dougal McGregor:
These months were to prove some of the most difficult of Minerva’s life, for it was then, aged only eighteen, that she proved herself truly her mother’s daughter, by falling head-over-heels in love with a Muggle boy.
He proposed to her, and she accepted. But she remembered the difficulty her parents had when her mother kept her magic secret, and so she cancelled the engagement and moved to London to work at the Ministry.
Husband. Her boss at the Ministry, Elphinstone Urquart, was a good friend. After she moved to Hogwarts, he proposed to her, but she declined. He proposed again in the aftermath of the First Wizarding War, and she accepted. Note that she kept her surname, which is why her marriage to Urquart can’t be worked out from the books:
Known to successive generations of students as ‘Professor McGonagall’, Minerva – always something of a feminist – announced that she would be keeping her own name upon marriage.
They didn’t have any children, but she does have some nieces and nephews:
The marriage (cut tragically short, though it was destined to be) was a very happy one. Though they had no children of their own, Minerva’s nieces and nephews (children of her brothers Malcolm and Robert) were frequent visitors to their home.
Unfortunately Urquart was killed by a Venomous Tentacula bite. As far as we know, Minerva never had another partner after this.
The books tell us about Hagrid’s parents (giant mother Fridwulfa, wizard father of unknown name) and his half-brother Grawp. Despite courting Madame Maxime in Goblet of Fire, the relationship didn’t work out (although they parted amicably) and Hagrid remained single:
Did Hagrid ever get married and have children?
[Aww from crowd] Oh, did Hagrid ever get married and have children? No. [awwws again] I may change that immediately due to the look on your face. Yes! He had 22! - No, no, Hagrid never did marry and have children.
Sort of a cheat, because he only becomes a Professor in the epilogue, but I like him, so let’s include him. We learn about his parents in the book (tortured to insanity by the Lestranges) and his grandmother (as far as we know, his only guardian). He would eventually marry fellow classmate Hannah Abbott:
Did Neville ever find love?
Of course. To make him extra cool he marries the woman who becomes, eventually, the new landlady at The Leaky Cauldron, which I think would make him very cool among the students, that he lives above the pub. He marries Hannah Abbott.
His entry in Pottermore has a field for family, and he’s described as “Unmarried, no children”. So cross him off your list.
She was married for a short time, with no children. Under “family”, her Pottermore entry reads:
Early marriage ended in unforeseen rupture when she refused to adopt the surname “Higglebottom”. No children.
J. K. Rowling had decline to answer in an interview whether any professors had spouses. We are not sure why exactly Rowling did that, but there is some speculation about this in the question Why exactly was information on Hogwarts Professors' spouses restricted?
This interview was before Order of the Phoenix was released. Since then, Professor Lupin had married in later books, but only when he was no longer a professor. Neville Longbottom would become a married Hogwarts professor according to some interview. We also know that Phineas Nigellus Black, a previous Headmaster of Hogwarts, has children: he calls Sirius his great-great-grandson in Order chapter 37, and we now know more of his family tree too.
We can be quite sure that Professor Dumbledore and Professor Snape do not have wives. It is very likely that Professor Lockhart has no family, for the hospital staff claimed in Order chapter 23 that he never gets visitors. I'm also sure that Rubeus Hagrid does not have a wife or children, for Harry was in sufficiently good standing with him that it would have come up somewhere in their discussions if he had one.
Other than these, I don't know anything about families of Hogwarts professors. I don't find it too strange that there is no mention though. From real life, I know I can be taught by teachers or professors for several years without ever learning about or meeting their family, for some people try very hard to keep their professional life and family separately.