Aspartame is commonly found in packaged foods like diet soda, sugar-free ice cream, low-calorie fruit juice, low-calorie yoghurt, gum and sugarless-candy.
It basically consists of aspartic acid and phenylalanine which are both naturally occurring amino acids. However, when broken down in the body, aspartame produces methanol. Methanol in large quantities can be toxic to the body, hence leading to the concept "aspartame poisoning". The quantity to cause this poisoning has never actually been produced in the human body though.
There are other speculative diseases linked to the intake of aspartame but there have not been sufficient scientific evidence to confirm or refute these claims.
However, this list is enough reason to avoid the artificial sweetener and stick to other natural alternatives.