Aspartame is an artificial sweetener used in some foods and drinks. First developed in 1965, it is often the subject of criticism by some people who believe it is harmful to humans - specifically that it can cause cancer. The chemical has been widely studied and a recent panel of experts set up by the European Food Agency concluded in 2013 that it is safe for human consumption at current exposure levels. Many other agencies, including the US FDA (after some years of problematic test methodology) have also passed it as safe.
Other effects that aspartame is claimed to cause are headaches, seizures, ADHD and a harmful change to breast milk. Numerous studies in these areas have again failed to highlight any specific concerns. Headaches are the interesting one here, as there is a wide range of literature on the subject, with views at each end of the spectrum and a lack of evidence or references to support various claims that it can directly cause symptoms.
So, probably best not to worry. Even levels of intake seen in some countries that are considered "high" are well below the acceptable daily intake accepted as a safe level of exposure.