High school teachers are probably less involved than elementary teachers, simply because high school students are thought of as slightly more independent and self-sufficient. That said, like many have posted, we are legally bound to report suspicion of things like abuse or neglect.
Otherwise, no, as a HS teacher, I try to stay out of the personal affairs of my students as much as possible. For the few students I build close personal connections with, I am always an open-door and a listening ear, but even then, I wait until a student seeks ME, rather than the other way around.
On the other hand, I will confront a sudden change in attitude if it is grossly affecting school work in MY CLASS. This, I've found, often results positively. Pulling a student aside at the end of class to say, "Hey, what's up? You look angry..." has usually ended up in a brief, but noteworthy conversation that allows my students to know I both notice, and care.