どういたしまして would be the translation of "You're welcome and いいえ／いえいえ for "No problem". Other common phrases you can use are こちらこそありがとう which means "Thank you too" and 恐縮（きょうしゅく）です used in business situations.

In this case, I taught a Taiwanese colleague to respond "ええで". Which means like "No worries." or "No problem.", but it is very casual expression in Japanese. "ええで" is a dialect from Kansai, Japan. So if you use it to your Japanese friends, it will be so funny. "ええ" should be stressed, and down to "で”. It's perfect intonation. Please remember, you can use it only your friends!

Usually, it will be ”どういたしまして”. When it comes to polite phrase, there is also "とんでもないですorとんでもございません".

It depends on its context and a relationship with a person who said thank you in Japanese. If you have a specific situation in mind, I love to share some examples.

Dear Igor-san, We don't usually say どういたしまして. I think we say 気(き)にしないで(no worries) instead. If it's business setting, we often say こちらこそありがとうございます. It really depens on..But if you help your friend and he/she says thank you to you, you can say いえいえ, 気にしないで, たいしたことないよ, etc. Thank you very much.