Aspartame in NutraSweet, Equal and AminoSweet is an artificial sweetener composed of 2 linked aminoacids: aspartic acid and phenylalanine. It is intensely sweet and although it may provide calories the amounts used to sweeten foods result in negligible effect.
There are numerous controversies about aspartame although it has passed the FDA requirements. These controversies are easily found on the internet and are simple assumptions that are not verified by science.
The concern is that the by-products of breakdown of aspartame can be toxic. The metabolism of aspartame leads to formation of formaldehyde, formic acid and methanol. The methanol is a neurotoxin but it is rapidly converted to formaldehyde. The formaldehyde is a known carcinogen but is rapidly converted to formic acid which is excreted in the urine.
The evidence suggests that the amounts of methanol and formaldehyde are too small to have a significant impact on health. What makes it controversial is the result of only one study conducted by the National Cancer Institute on rats. It showed that when female rats are fed high aspartame diet they have a higher incidence of Lymphomas and Leukemias. This association was never found in human studies.