I translate it by "Oh mon Dieu" But my level in English is not excellent. I have looked at the website WordReference, Here are other answers. http://forum.wordreference.com/threads/oh-dear.213478/

'Mon Dieu', perhaps, if it's shock or surprise? 'Zut alors' if it's annoyance? 'Oups' if you've done something stupid? These are guesses. Waiting for a native French speaker to confirm!

"Mon cher" for a guy or "Ma chère" for a girl. You can also put "très" in order to insist ! For example : Mon très cher amour, je vous aime My "very" dear love I love you