Medical intravenous administration connectors include a first coupling member having a female luer, a valve member having a substantially rigid stem and a substantially resilient body with a sealing surface, and a second coupling member having a fluid coupling extending from one end and an internal valve member support. The coupling members are structured to couple to each other with the valve member being biased to a closed position. When assembled, the valve stem extends into the female luer, and the valve body biases the sealing surface against an annular ring in the first coupling member thereby blocking fluid communication. Preferably, vanes are provided in the second coupling member on which the resilient body of the valve sits, with the vanes acting as a centering mechanism for the valve. The valve may be opened for fluid flow through the assembly by coupling a male luer to the female luer of the assembly, or by pressure actuation. Several valve members are disclosed and several structures for mating the first and second coupling members are disclosed. Y-injection sites and intravenous manifolds utilizing the valve arrangement and coupling members of the invention are also disclosed. All embodiments are easy to prime, limit priming volume, and are arranged without dead-spaces in which blood can be trapped.