Raspberry is a delicious fruit with important nutritional and health properties for consumers. The efficiency of achieving raspberry breeding aims such as productivity, fruit quality, and adequate response to stressors, etc., depends directly on knowledge of the inheritance of traits and genetic factors of influence and their pragmatic use. In this study, the main morphological characteristics and chemical components of fruits of 24 raspberry genotypes were studied in a comparative field trial; 14 were promising selections and the other 10 included their parental forms (Autumn Bliss, Glen Moy, Glen Prosen, Opal, Pathfinder, Titan, Tulameen, Veten, Willamette) and Glen Ample cultivar, which was used as control. The results highlighted significant differences and a large variation among the genotypes (between 2.40 and 4.90 g for fruit weight, 0.19–0.47 kg/cane for yield, 50–106 for drupelets/fruit, 10.0–12.7% for dry matter, 0.23–2.00% pectin, 1.61–2.72% glucose, etc.). The inheritance of the analyzed traits, considered quantitative, was different, but a low heritability was recorded for non-marketable fruits and the number of drupelets in fruit. In several hybrid selections, negative heterosis prevailed, highlighting the breeding difficulties of the important desired traits of the species. The values of heterosis and the broad-sense and narrow-sense heritability of some traits demonstrate that, through judiciously choosing parents, raspberry breeding in the desired direction can be successful.