New to iOS 7 is the ability to block people. This prevents you from receiving regular phone calls, FaceTime audio and video calls, text messages, and iMessages from people on your blocked list. If someone does call they will be sent directly to voicemail, you won't be notified if they do leave a voicemail, and that voicemail will goto a special "Blocked" bucket that you don't ever have to deal with.
Setup is simple - for people already in your address book go into Settings, then to Phone and select Blocked. From here you can add someone to your Blocked list using the "Add New..." button. You can now delete this person from your address book, and they will remain on your Blocked list.
If you don't have someone saved in your address book, but have received a call from them goto your Recents list, then tap the 'i' to the right of their entry and scroll to the bottom, then tap "Block this Caller". The same can be done for someone texting you - tap "Contact" in the top right of a message, then tap the 'i' and select "Block this Caller" from the bottom of the screen.
Did someone redeem themselves and is now worthy of communication with you? To remove them from your blocked list go into Settings, then to Phone and select Blocked. Then swipe left over the entry in your blocked list to reveal a red "Unblock" button; tap this button.