There is an interesting thread on reddit titled: "When did you realize that you were an adult". I still feel that I haven't quite reached that realization yet. I've come close though.
During 2nd year into my master's, I was guiding a tour of the University's Robotics lab for middle school kids. After wowing them with some cool robots, I let them play with some of them. One of the little girls came up to me and asked shyly
Sir, Can I shake your hand?
I was blown away by the question. I said "Of course" and shook her hand. She seemed impressed with herself and walked away, making me realize some of these kids actually think I'm a scientist.
I still feel this way:
I've successfully postponed any purchase that could make me feel like an adult, a TV, Couch, House.
It's only a matter of time.