1. Of oneself, to regret having ever existed, as due to some extreme suffering one is or will be experiencing. Basic training in the military is so hard that you'll often find yourself cursing the day you were born. She was so embarrassed by the event that she cursed the day she was born.

2. To detest someone to such a degree as to wish they had never existed. You're just a horrible, selfish pig, and I curse the day you were born!