This paper reports new addition reactions of oxetanes with certain protonic reagents such as carboxylic acid, phenol, and thiol, and with certain aprotic reagents such as acyl chloride, thioester, phosphonyl dichloride, silyl chloride, and chloroformate using quaternary onium salts as catalysts. The kinetic study of the addition reactions of oxetanes was also investigated. These new addition reactions were applicable to the synthesis of new polymers. These polyaddition systems could also construct both polymer main chains and reactive side chains. The alternating copolymerization of oxetanes with carboxylic anhydride was performed. Furthermore, it was found that anionic ring-opening polymerization of oxetanes containing hydroxy groups proceeded to afford the hyperbranched polymer (HBP) with an oxetanyl group and many hydroxy groups at the ends of the polymer chains. Alkali developable photofunctional HBPs were synthesized by the polyaddition of bis(oxetane)s or tris(oxetane)s, and their patterning properties were examined, too. The photo-induced cationic polymerization of the polymers with pendant oxetanyl groups and the thermal curing reactions of polyfunctional oxetanes (oxetane resins) were also examined to give the crosslinking materials quantitatively.