If you only have time to visit one religious site in the Kathmandu Valley, I highly recommend that you consider Swayambhunath. Set on a hill that offers sweeping views of the valley, this Buddhist stupa dates from the 5th century.
Legend declares that the valley was once a gigantic lake (geologists agree with this part) and in ancient times a perfect, radiant lotus blossom appeared in the midst of the lake. The gods proclaimed the blossom to be Swayambhu ("Self-Created"). As supernatural forces drained the lake, the lotus flower settled on the top of the hill that now houses the great stupa.
Swayambhunath is so sacred that it is said that worshiping here carries 13 billion times more merit than anyplace else. In the morning and toward the end of the day, Swayambhunath comes alive with worshipers practicing their sacred rituals. In addition to the domed stupa itself, there are many other temples and shrines of varying styles.
For photographs of another sacred Buddhist stupa (chorten) in Kathmandu, visit the Bodhnath page.