I do feel when people experience things... not always the SAME things they feel, but I do imagine myself in their situation (sometimes a little too vividly...) and act according to how I would feel in that situation, so long as I can imagine myself in that situation.
Unfortunately, when I don't quite understand the situation and how one found themselves in such a position, I tend to ask a lot of questions, which to some comes off as being insensitive. I can't feel a certain way JUST because that other person over there looks like they're feeling that way - I need to know why, or feeling as such doesn't make sense!
On the other hand, when I do understand someone's situation enough to feel it, some emotions are easier for me to feel, handle and express than others - anger is a lot more manageable for me than straight sadness or resignation, and sometimes with those "easier" emotions I go too far, feeling more than the person actually affected does. That's gotten me in trouble sometimes.