Interesting reading through the responses... "thank you" and " thanks" are both acknowledged as formal or less formal, with "thank you" coming in first.
"You are welcome" is almost never used unless you add a word, i.e. "you are very welcome". "You're welcome" wins out over both alternatives. I suspect that most of us use the contraction rather than the long form without thinking about it. It probably bodes well for "no problem". Language is a living thing.