That's a great question. I agree with Eva that in text it's unnecessary, unless you have something extra to say.
In speech, I feel that "you're welcome" is rather formal. Here are some variations on replying to thank you:
[It was] my pleasure
Note that in English "thank you" is always necessary when talking to someone you don't know well, even for tiny favours, eg. passing the salt at the dinner table.
However in this instance you don't need to say anything. Personally, if I thanked someone for passing the salt and they replied "You're welcome" it would feel strange, as such a minor act doesn't require such a formal reply.
Contract it to 'you're welcome' if you're going to say it. It's really quite rare for native speakers to use the full form.
No I don't think it's a must but it's a nice thing to do.