Background: Hypodontia represents a notable clinical and public health concern. Objective: To assess the prevalence of congenitally missing permanent teeth in a sample of orthodontic/dental patients of Caucasian origin originating from the Greek island of Lesvos. Materials and Methods: Panoramic X-rays from 621 children and adolescents, aged 9 to 16 years (average age 12.5 years), 521 seeking orthodontic care (orthodontic group) and 100 seeking dental care (non-orthodontic group) were examined to identify congenitally missing permanent teeth. Results: The orthodontic group exhibited a 5.5% prevalence of congenitally missing permanent teeth (2.8% females; 2.7% males), while the non-orthodontic group showed a prevalence of 4% (3% females; 1% males). The descending order of prevalence for missing tooth types was as follows: lower second premolars, upper laterals, lower central incisors, lower canines, upper second premolars, and lower second molars. Among orthodontic patients with missing teeth, 62% presented with an Angle’s Class II malocclusion. Hypodontia was most frequently observed in the mandible. No statistically significant differences were observed between the orthodontic and non-orthodontic groups in terms of the percentage of children and types of congenitally missing teeth. Conclusions: Congenitally missing teeth were observed in about 4–5% of the studied population with a female predilection. The lower second premolar was the most commonly absent tooth, followed by the maxillary lateral incisors. An Angle’s Class II malocclusion was present in the majority of orthodontic patients with hypodontia, mostly in the mandible.