I once had a potential client come in for an opinion on a lawsuit and i did some research - The file is in storage but some of what I found out:
Aspartame has undergone over 200 scientific tests since 1967. These test have been done on men, women, children, and animals. It has been approved by the United States Food and Drug Administration, Canada's Health Protection Branch, the World Health Organization, and over 100 other regulatory nations (1).
A study was done to determine the long term effects of aspartame intake. In this study, 108 men and women, ages 18 to 62, volunteered to be part of a double-blinded, placebo-controlled experiment. During this 24 week study, some volunteers were given 75 mg of aspartame for every kg of body weight a day. No lasting changes in vital signs, body weight, or other side effects were noted. The results from this test show aspartame to be safe (2).
People often complain of headaches after consuming a product that contains aspartame. A study was done to see if these complaints were accurate. This study was a double-blind, placebo controlled test. The results show that aspartame is no more likely to cause a headache then placebo (3).
The only "evidence" seems to be anecdotal. One resercher even suggested that the claimed symptoms were caused by hearing about others with syptoms.