We've been eating most fats long before heart disease and cancer was prevelant. I'm a strong believer that it's the artifical fats (the one's that everyone told you were good for you - like margarine or mayo) such as hydrogenated or partially hydrogenated (trans fats) - are the ones doing the damage - and they're in A TON of stuff we eat.
I think there are good fats. Because fat is so calorie-dense, it's easy to take in more than you can utilize (hence adds to fat problem - more from too many calories than the fat itself).
You want to be concerned about "fat" for other reasons. Read this and understand it: http://www.qfac.com/articles/dioxins.html . THERE'S NO WAY FOR YOUR BODY TO GET RID OF THIS!!!!! This is NOT like so many bad things that cause "free-radical" damage, which there are plenty of good anti-oxidants that will take care of this. I've been told about dioxins before, but after reading about it THIS TIME (AGAIN), it really hit home.