Background/Objectives: Radial artery occlusion (RAO) is the most common complication of transradial coronary catheterization. In this study, we aimed to evaluate the incidence of RAO and identify the risk factors that predispose patients to it. Methods: We conducted an investigator-initiated, prospective, multicenter, open-label study involving 1357 patients who underwent cardiac catheterization via the transradial route for angiography and/or a percutaneous coronary intervention (PCI). Univariate and multivariate logistic regression analyses were performed to identify potential predictors of RAO occurrence. Additionally, a subgroup analysis only for patients undergoing PCIs was performed. Results: The incidence of RAO was 9.5% overall, 10.6% in the angiography-only group and 6.2% in the PCI group. Independent predictors of RAO were as follows: (i) the female gender (aOR = 1.72 (1.05–2.83)), (ii) access site cross-over (aOR = 4.33 (1.02–18.39)), (iii) increased total time of the sheath in the artery (aOR = 1.01 (1.00–1.02)), (iv) radial artery spasms (aOR = 2.47 (1.40–4.36)), (v) the presence of a hematoma (aOR = 2.28 (1.28–4.06)), (vi) post-catheterization dabigatran use (aOR = 5.15 (1.29–20.55)), (vii) manual hemostasis (aOR = 1.94 (1.01–3.72)) and (viii) numbness at radial artery ultrasound (aOR = 8.25 (1.70–40)). Contrariwise, two variables were independently associated with increased odds for radial artery patency (RAP): (i) PCI performance (aOR = 0.19 (0.06–0.63)), and (ii) a higher dosage of intravenous heparin per patient weight (aOR = 0.98 (0.96–0.99)), particularly, a dosage of >50 IU/kg (aOR = 0.56 (0.31–1.00)). In the PCI subgroup, independent predictors of RAO were as follows: (i) radial artery spasms (aOR = 4.48 (1.42–14.16)), (ii) the use of intra-arterial nitroglycerin as a vasodilator (aOR = 7.40 (1.67–32.79)) and (iii) the presence of symptoms at echo (aOR = 3.80 (1.46–9.87)), either pain (aOR = 2.93 (1.05–8.15)) or numbness (aOR = 4.66 (1.17–18.57)). On the other hand, the use of intra-arterial verapamil as a vasodilator (aOR = 0.17 (0.04–0.76)) was independently associated with a greater frequency of RAP. Conclusions: The incidence of RAO in an unselected, all-comers European population after transradial coronary catheterization for angiography and/or PCIs is similar to that reported in the international literature. Several RAO prognostic factors have been confirmed, and new ones are described. The female gender, radial artery trauma and manual hemostasis are the strongest predictors of RAO. Our results could help in the future identification of patients at higher risk of RAO, for whom less invasive diagnostic procedures maybe preferred, if possible.