As with the tombs, there are more pagodas surrounding Hue than you can shake a stick at. If you're only going to see one pagoda, make it Thien Mu. It's situated in a beautiful spot over looking the Perfume River, on the river road that runs along the north bank, about 3.5km west of the railway bridge.
Built in 1844 by Emporer Thieu Tri, it features some golden Buddha images at the base, along with a big bell cast in 1710, and a stone turtle holding a marble stele inscribed in the 17th century. In 1963 a Buddhist monk named Thich Quang Duc shocked the world by travelling to Saigon, pouring a can of gas over his head, and lighting himself on fire, in protest of American interference in South Vietnam's self-determination. The image of a robed man, sitting cross-legged on the pavement, rocking back and forth in meditation as he was consumed by flames, was broadcast on American television. It was the first in what would be a long series of disturbing images brought into American homes during the world's first TV war -- images that would eventually ignite a backlash against the war, and lead inevitably to the American withdrawal, and the north Vietnamese victory.
The monk in question hailed from this particular pagoda, which still functions as a monastery to this day. The Austin motorcar he used to drive down to Saigon is on display in the sanctuary in back.