A needle (26) is provided that can be used for introducing or aspirating fluids to a patient or as an introducer needle for positioning and inserting a catheter (58), such as a peripheral IV catheter into a patient. The needle (26) can be an introducer needle that extends from the distal end of the catheter during insertion. The needle (26) has an insertion tip with a configuration to assist penetration into a vein (60) with a reduced incidence of injuring the inner surface of the vein or inadvertently passing through side wall of the vein. The needle tip (46) can be formed with a curved distal end surface (54) where the pointed tip (46) is spaced radially inward relative to the outer surface (56) of the needle (26). In another embodiment the needle tip can have a reverse beveled surface (42, 44) having an axial length, angle, and curvature to assist in penetrating the vein with a reduced incidence of transfixing the vein.