This one is dead now (the SIL, not my MIL), but she gets top billing in my memory for insensitivity.
My MIL was diagnosed with ovarian cancer about 12 years ago. She had radiation treatment (some in-patient, some out-patient) and was continuing to work her full-time job as a nursing supervisor during the treatment (this was right around Christmas time). Her SIL (who had always been a prima dona) came to stay with them for a long weekend during the treatment so she could "help" MIL.
I'm about 6 months pregnant at the time, and MIL has just come home from her radiation treatment, which she had scheduled to take AFTER completing her night shift of work (the SIL was still in bed when I got there, which was about the time MIL made it home). When I got there and this lady got up, I fixed her breakfast (and tried to encourage Mom to eat something before she went to bed).
MIL, her SIL, and I are sitting at the kitchen table, and the SIL in question says several times "Boy would a glass of iced tea taste good." After about the fourth time, MIL says "Would you like me to make you some iced tea?" Her SIL has the nerve to say "oh, would you please?"

I jumped up and made the tea and told MIL to go off to bed as I knew she was tired. I just couldn't believe that the SIL would do this! I grabbed my FIL (it was his sister) and told him that if he didn't suggest that his sister go home, then I was going to! She left that afternoon, after many "Are you sure you don't want me to stay and helps".
I can't believe how much this still bugs me, 12 years later! Of course, the fact that my MIL is one of the most special, giving, loving people I know contributes to this feeling!