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:
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:
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:
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:
Fiancée. After leaving Hogwarts, she fell in love with the son of a Muggle farmer, called Dougal McGregor:
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:
They didn’t have any children, but she does have some nieces and nephews:
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:
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:
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:
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.