When my sister died I felt like people simply saying they were sorry was a really nice thing. But I didn't like people to feel uncomfortable (ok it was a little funny to see the big managers come at the same time to tell me they were sorry, because you could just tell they were supporting each other through the awkwardness, ha).
The worst thing said to me was from some friend of hers (I assume it was a friend, there were a lot of people gathered at my brother-in-law's so might have been a friend of his) who made a rather insulting comment about my levity and it being hard to believe I was her sister the way I was acting like that.
I was too young when my uncle died to have an opinion, but my father was still annoyed years later remembering and complaining about the comments after his brother died. As near as I could tell, the comments were along the line of 'don't take it so hard, he's in a better place' and my dad didn't feel they cared about his feelings at all and/or he was having the wrong feelings in their opinion.