Naturally I get offended but if it's someone I really don't have to talk to on a daily basis or someone I barely know I'll ignore it. Unless it really rustles my jimmies, then you better watch out cause i'm going to insult you back until you cry.
If it's a family member or something... depending on the severity, i'll shrug it off or confront them about it and tell them I don't appreciate what they said.
edit: I do tend to get more offended when my friends are insulted though. If they're around I will let them defend themselves but don't try and talk smack about my friends to me behind their back, they're my friends for a reason and you better shut your mouth.
If it's a family member or something... depending on the severity, i'll shrug it off or confront them about it and tell them I don't appreciate what they said.
edit: I do tend to get more offended when my friends are insulted though. If they're around I will let them defend themselves but don't try and talk smack about my friends to me behind their back, they're my friends for a reason and you better shut your mouth.