I have invited two students for dinner one evening next week, and I'm really looking forward to it. The senior is someone I have spent time with before through German-club activities. She also came over one evening to watch Labyrinth with me (one of my favorite movies), but it's been a while since we hung out. The other is a freshman who recently became my advisee, and is coming out of the foster care system. She works in the library and is one of the sweetest students I've met. She let me tag along with her to see the Twilight premier last November.
I love the position of librarians, at least here, to do stuff like this. If I were a professor, I'd have to invite a whole class, or a club. I guess there are lines to openly having favorite students, but I'm still more free as a librarian. I know the students really enjoy a home-cooked meal, and I enjoy their company.