Visiting the marble shrine of Muslim Sufi saint Nizam-ud-din Auliya is Delhi's most mystical, magical experience. The dargah is hidden away in a tangle of bazaars selling rose petals, attars (perfumes) and offerings, and on some evenings you can hear the qawwali (Sufi devotional singing), amid crowds of devotees. The ascetic Nizam-ud-din died in 1325 at the ripe old age of 92. His doctrine of tolerance made him popular not only with Muslims, but with adherents of other faiths, too.
Later kings and nobles wanted to be buried close to Nizam-ud-din, hence the number of nearby Mughal tombs. Other tombs in the compound include the graves of Jahanara (daughter of Shah Jahan) and the renowned Urdu poet Amir Khusru. Scattered around the surrounding alleyways are more tombs and a huge baoli (step-well). Entry is free, but visitors may be asked to make a donation. You must remove your shoes before entering the shrine, but there's no need to do so whilst wandering the bazaars that approach it, despite pushy shoe keepers telling you otherwise; follow the lead from visiting locals.
A tour with the Hope Project, which ends at the shrine, is recommended for some background.