Minerva McGonagall is the head of Gryffindor (Harry's dormitory house), and fills in as headmistress on occasion throughout the series. She is both strict and caring. She also has a great sense of humor. I especially love the scenes between her and Dolores Umbridge, who is a quite awful person.
McGonagall, however, does not put up with Umbridge's crap the way some teachers do. She is not afraid of Umbridge in the least either.
Other than putting down Umbridge, she is watchful of harry and is always concerned about his well-being. She has a soft spot for him, which many people, real and fictional, do.
McGonagall can also transform her physical appearance (I noted in Tonks entry that she can as well). However, McGonagall cannot alter her human physical attributes; she can turn into a cat though. She is an animagus. This helps her to disguise herself as it does Tonks. We first meet McGonagall early in Sorcerer's Stone as a cat sitting outside the Dursley's house before Harry even shows up.
My favorite scenes with McGonagall are the ones where she interacts with Umbridge, so instead of one McGonagall quote, I'm going to add a few that I like.
Probably my favorite, when McGonagall tells Harry he could work for his ambition of becoming an Auror.
"I doubt it will make much of a difference," said Professor McGonagall coldly, "unless a mad axe-man is waiting outside the doors to slaughter the first into the entrance hall."
When Umbridge insists Marietta Edgecomb told her something and Marietta begins to deny it...
"Well, usually when a person shakes their head," said McGonagall coldly, "they mean 'no.' So unless Miss Edgecombe is using a form of sign language as yet unknown to humans --"