Inspired by methods of wet fiber spinning, we introduce a process using a 3D printer to create dense carbon nanotube (CNT) fibers and extensible coils with metal-like DC specific conductivity. An extrusion-based printer with an immersed nozzle extrudes a homogeneous shear-thinning ink (with initially < 1 % CNT concentration in water) into a liquid bath of antisolvent, inducing immediate precipitation-driven solidification slightly beyond the nozzle tip. This process forms continuous fibers of CNTs with conductivity up to 3 × 105 S/m, exceeding that of dense graphite and approaching that of CNTs spun from similar inks in a continuous fiber spinning process (6 × 105 S/m). The specific conductivity is up to 1 × 103 S m2/kg, comparable with gold (2.3 × 103 S m2/kg). The printing regimes are analyzed, with consideration of the draw ratio imposed during printing. Particular focus is placed on adjusting the speed of counter-diffusion of the ink solvent and the bath liquid, which allows for tuning of fiber diameter, conductivity, and specific conductivity respectively over ranges of one, four, and five orders of magnitude. The conductivity of resulting fibers is maximized when the speed of solvent counter-diffusion is high and the radius reduction is largest. When extrusion speed is also high relative to speed of the nozzle motion, a fluid mechanical coiling instability emerges which creates filaments with periodic coils, allowing for intricate designs to be formed along a linear extrusion path. Once dried, these densely coiled structures initially maintain their shape and can subsequently undergo up to 50 % strain with under 1 % change in resistance and 170 % linear extension with 20 % increase in resistance as the coils unwind. The resulting complex coil structures have applications in lightweight circuitry and as flexible interconnects.