We describe microRaman studies of serpentine single-walled carbon nanotubes grown on single-crystal quartz. Local Raman spectra were collected from bent and straight segments of the same nanotube to elucidate the effects of bending. Bending radii as large as 1--2 $\ensuremath{\mu}\text{m}$ produce a measurable shift of the frequencies of the G, D, and 2D bands while the radial breathing mode remains nearly unaffected by bending. The frequency shift is approximately linear in the bending curvature $1/{R}_{\text{b}}$ for radii of curvature ${R}_{\text{b}}$ between 0.6 and $3.0\text{ }\ensuremath{\mu}\text{m}$. A very tightly bent bundle with ${R}_{\text{b}}\ensuremath{\sim}50\text{ }\text{nm}$ develops a very intricate G-band structure caused by new Raman modes that are activated by the broken cylindrical symmetry. These results show diverse behavior depending on the nanotube wrapping indices $(n,m)$ but are comparable in magnitude to those predicted by tight-binding calculations of the Raman response in bent tubes.