(1) Background: We aimed to identify the possible relationship between various diseases of the upper digestive system and colon polyps by analyzing patients with gastric polyps and evaluating the cancers and diseases accompanying the polyps. (2) Methods: Each patient’s age; gender; polyp type and size; presence of Helicobacter pylori (H. pylori), atrophic gastritis, and intestinal metaplasia; status of whether cancer developed during follow-up; status of whether a colonoscopy was performed or not; and colon pathologies detected during colonoscopy were analyzed retrospectively using hospital records. (3) Results: Between the study dates, 19,214 esophagogastroduodenoscopies were performed in the endoscopy unit of our hospital. Gastric polyps were detected in 178 (0.9%) patients. No significant relationship was found between the gastric polyp size and the occurrence of gastric cancer or gastrointestinal system malignancy (p > 0.05). A colonoscopy was performed in 86 of the 178 patients who underwent gastroscopy. The frequency of polyp detection during colonoscopy was statistically significantly higher in patients with gastric polyps than in patients without gastric polyps (p < 0.001). (4) Conclusions: New prospective studies are needed regarding the relationship between gastric polyps and gastrointestinal system diseases. Going forward, a colonoscopy will be required in gastric polyp patients, especially with FGP.