We all blow it from time to time—whether by breaking a promise, being irritable and short-tempered, or wrongly accusing our kids. If we hurt our child's feelings, simply acknowledging, "I'm sorry. I was wrong. Will you forgive me?" can mitigate much of the damage.
A sincere apology not only conveys respect for your child and shows that you value her, it also helps her learn compassion and that no one is perfect. She'll be more likely to admit her own shortcomings if she can expect you to forgive her.
If you find yourself apologizing over and over for the same offense—such as punishing your child too harshly—think about why you keep repeating the behavior. If you need to find better ways to handle your temper, for example, you could talk to a trusted friend, your pediatrician, or your pastor or rabbi to get some advice. Repeating "I'm sorry" won't mean anything if you can't show your child you're willing to change.