(1) Background: Cognitive features of patients with amyotrophic lateral sclerosis (ALS) have never been specifically analyzed according to the lateralization of motor impairment. In the present study we investigated the cognitive performances of ALS patients to describe the relationship between motor and cognitive dysfunction, according to site and side of disease onset. (2) Methods: Six-hundred and nine ALS patients underwent a comprehensive neuropsychological evaluation at diagnosis in Turin ALS Centre Tests included—mini-mental state examination (MMSE), frontal assessment battery (FAB), trail-making test A/B (TMT A-B), digit span forward and backward (digit span FW/digit span BW), letter fluency test (FAS), category fluency test (CAT), Rey auditory verbal learning test (RAVLT), Babcock story recall test (BSRT), Rey-Osterrieth complex figure test (ROCFT), Wisconsin card sorting test (WCST), Raven’s coloured progressive matrices (CPM47). Cognitive performances of patients, grouped by side and site of onset, were statistically compared using z-scores, as appropriate. (3) Results: Bulbar patients and bilateral spinal onset patients (Sbil) were generally characterized by lower cognitive performances in most neuropsychological tests, when compared to patients with lateralized onset (right-side spinal onset, Sri and left-side spinal onset, Sle). Digit span backward and visual memory task (ROCFT) median z-scores were significantly higher, reflecting a better cognitive performance, in Sri patients when compared to bulbar/Sbil patients, while verbal memory tasks (RAVLT and BRST) resulted in significantly higher scores in Sle patients. Our results are in keeping with hemispheric functional lateralization of language and visuospatial abilities. (4) Conclusions: In ALS patients, as in other neurodegenerative diseases, we found a direct relationship between lateralized motor and cognitive features.