A bicycle wheel basically has a hub, a plurality of spokes extending outwardly from the hub and an annular rim coupled to the outer ends of the spokes for supporting a tire. The annular rim has a spoke attachment portion with a plurality of openings for receiving the outer ends of the spokes therein. The outer ends of the spokes are bent such that first sections of the spokes are offset from sections of the spokes. These bends are positioned in the openings of the rims to retain the outer ends of the spokes in the openings of the rim. In selected embodiments, a fastener or an adhesive may be used to more securely retain the outer ends of the spokes in the openings of the rim. In certain other embodiments, the spoke attachment portion of the rim can be constructed of individually spaced elements which can be either fastened to the rim or unitary part of the rim.