The tree you're thinking of is likely the weeping willow (Salix babylonica). It's known for its graceful, cascading branches that hang down towards the ground like weeping hair.

While the weeping willow is the most famous example, other trees with downward-growing branches include:

* Weeping cherry (Prunus subhirtella 'Pendula')

* Weeping beech (Fagus sylvatica 'Pendula')

* Weeping birch (Betula pendula 'Youngii')

* Weeping elm (Ulmus glabra 'Pendula')

These are just a few examples, and there are many other trees with weeping forms. The term "weeping" generally refers to any tree with branches that droop significantly downwards.