Globally, more than 322 million people are living with depression, with a considerable percentage driving while under the effects of such impairments. Their impacts on specific parameters of driver behavior and road safety, such as driver speed and reaction time, however, remain understudied. The literature indicates that driving performance deteriorates in patients with depressive symptoms, causing increased crash probability and more aggressive behavior. The objective of this research was to examine the influence of neurological diseases on driving performance, and particularly, how depression affects reaction time and the standard deviation of driving speed. Data were obtained from a large-scale simulator study comprising 12 driving urban and rural trials. The sample consisted of 113 impaired participants, suffering from mild cognitive impairment, Parkinson’s disease, Alzheimer’s disease, and depression, and 92 people with no cognitive impairments as the control group. Inclusion criteria comprised having a driving license and driving experience (≥3 years), being active drivers, not having critical psychosis, eye or motor disorders, and not having drug/alcohol addictions. Analysis of cognitive impairments based on GDS questions showed that frequent ‘feelings of boredom’ correlated with a 7% increase in reaction time and a 8% increase in the standard deviation of driving speed. Conversely, ‘feelings of worthlessness’ reduced the standard deviation of driving speed by 4.5%. ‘Feeling full of energy’ contributed marginally significant increases to reaction times of 4%. Drivers with Alzheimer’s and Parkinson’s diseases showed higher reaction times, while drivers with depression and the control group showed lower reaction times. Drivers with Parkinson’s disease showed statistically fewer deviations of average speed. This research shows that cognitively impaired individuals have larger reaction times and more erratic driving speeds. Present findings can be used to inform both patients and authorities of their driving behavior and can be considered when (re)issuing driving licenses.