Background/Objectives: The purpose of this study was to measure the bone thickness and angulation of the maxillary and mandibular anterior teeth on the buccal and palatal/lingual sides and also to analyze the sagittal root position (SRP) in the alveolar bone in relation to age and gender using cone-beam computed tomography (CBCT) in an Iraqi subpopulation. Methods: CBCT images of 1200 maxillary and mandibular central and lateral incisors and canines from 100 patients (48 males and 52 females) were retrospectively analyzed. These patients were categorized by age into group I ≤ 25, group II 26–40, and group III ≥ 41 years old. The SRP in the alveolar bone was classified as class I, class II, class III, and class IV, and the buccal type was further classified into subtypes I, II, and III. In addition, the buccolingual inclination of the tooth and buccal/palatal/lingual bone thickness at the coronal, middle, and apical thirds were evaluated and then compared based on age and gender. The data were analyzed using the Pearson chi-square test. Descriptive statistics, Kruskal–Wallis and Mann–Whitney U test were used to compare the thickness and angulation according to the SRP classes. Results: The mean frequency distribution of SRP of maxillary anterior teeth indicated that most of them were located buccally and were classified as (Class I) and subtype (III). Moreover, for mandibular anterior teeth, the majority were classified as (Class IV) and subtype (II). The mean sagittal angulation of maxillary anterior teeth approximately ranged from 5.9 for tooth 12# to 8.2 for teeth 13# and 23#, while for mandibular anterior teeth it ranged from 7.4 for tooth 33# to 10.3 for tooth 41#. The thickness of bone in the apical third of the buccal side of all maxillary and mandibular teeth was significantly related to age (p < 0.05). In the middle third, the thickness of bone in the buccal and palatal side of all maxillary anterior teeth and in the apical third of most mandibular teeth in the lingual side was significantly higher in males (p < 0.05). Conclusions: A majority of the maxillary anterior tooth roots were positioned close to the buccal cortical plate, while most of the mandibular anterior teeth were engaging both the buccal and lingual cortical plates. Males had more alveolar bone thickness for both maxillary and mandibular anterior teeth, and only the apical portion significantly changed with age. CBCT of the buccal and palatal/lingual bone and SRP is recommended for the selection of the appropriate treatment approach and implant placement.