Single-mode polymer photonics is of significant interest to short-reach data communications, photonic packaging, sensing, and biophotonic light delivery. We report here experimental demonstration of mechanically flexible waveguides fabricated by using commercial off-the-shelf biocompatible polymers that claim a record low propagation loss of 0.11 dB/cm near 850 nm wavelength. We also show the excellent flexibility of the freestanding waveguides which can withstand repeated deformation cycles at millimeter bending radius without compromising their low-loss characteristics. High-performance passive optical components, such as waveguide Y-branches, multi-mode interferometers (MMIs), and waveguide crossings are also realized using the polymer photonics platform.