This is related to the recent entry in the web comic xkcd: http://xkcd.com/945/
I never say, "I'm sorry," because people interpret that as if I feel at fault, when I don't.
I've been simply saying, "that sucks," or, "that is very unfortunate".
If someone dies you can say, "my condolences," and it's perfect; however, that obviously can't be used in a situation not involving death, like in the comic.
Preferably I'd like something like, "I'm [x]," or, "I give you my [x]."
I suppose sympathetic/sympathies would work, but is there any other word or phrase, perhaps something less aggressive so as to be unlikely to be considered sarcastic?
I personally find myself feeling awkward every time this comes up.
EDIT: Keep in mind, I very much dislike adding unnecessary bias to my reply. So saying things like, "that's terrible," is not something I'm a fan of doing. What if it was an icy day and the bus came 20 minutes late? I wouldn't say that's terrible, because I'm implying the bus did a terrible job, when it probably did a great job keeping it's passengers safe.
Best Answer
What is your problem with condolence? It does not only apply to grief of death, but of any severe suffering. Its origins are similar to sympathy and compassion, all meaning essentially to suffer together (or as the commenter said "I feel your pain.")
However, all three of these words seem to work: I offer my sympathies, or condolences. I'd also say that to say "I'm sorry" only means "I apologize" in some circumstances. "I'm sorry for the terrible thing happening to you" does not in any way imply that you feel responsible, or are accepting any blame.