Good question and I think a question that everyone out there tends to have differing opinions on.
I would just like to add my two cents about Aspartame and other artificial sweetners in regard their usage, weight management and possible complications. From my experience dealing with clients that have struggled with their weight and particularly sugar cravings.
I believe It's okay to have a little bit a day (everything in moderation, right?) but having litres of diet soft drinks or other diet foods would not be advisable. Basically artificial sweeteners although they have zero calories, can actually be up to 200 times sweeter than sugar in itself. When this is tasted on the tongue, the brain actually is primed to look for more sugar. So is it really solving your sugar craving?
To add a second point there is some evidence that large amounts can cause mitochrondrial damage in cells, this is very large amounts though but still. I guess to sum up if you are finding that you need to use large amounts of it to lose weight it can actually a reverse effect in terms of your body will still be craving sugar and ultimately you will give in to that craving and over time you could gain weight. This gain in weight and body fat over time as common knowledge can lead to chronic diseases such as diabetes, cardiovascular disease and certain cancers.
What to do instead?
I believe finding sweet options from NATURAL sources of sugar such as fruit, dairy products and honey to name a few. A little bit of sugar is OK it's just too much that can be a problem. So I guess to sum up. As posters have said, having some sweetners in your diet is not directly linked to chronic diseases such as cancer HOWEVER I still don't think having too much of anything would be advisable for the reasons I have stated above.
Hope that helps.