What is the least dense material known to man?

Graphene aerogel.

(Graphene aerogel being balanced on a blade of grass!)

Air has an approximate density of 1.2 kg/m^3, and graphene aerogel is seven times lighter than (an equivalent volume of) air. This material was successfully synthesised by researchers at Zhejiang University, China. The precursor materials used were graphene (which is a single layer of sp2-bonded carbon atoms) and carbon nanotubes or CNTs (single/ multiple rolled-up sheets of graphene). A solution of these two materials is poured into a suitable told and subjected to "freeze-drying". Freeze-Drying is a process where one reduces the temperature of a material to freeze it, and then reduces the surrounding pressure, so that the liquid phase (which freezes into a solid) then undergoes sublimation to the gas phase. This route avoids the direct liquid-gas transition (involved in usual drying).

Freeze-drying results in high dehydration of the 'graphene+CNT' mixture and results in a structure where the carbon atoms of graphene monolayers supported by a framework of CNTs. The final product has a measured density of 0.16 mg/cc, with good absorption properties. This has been purported to have usage in cleaning oceanic oil spills.

(A graphene aerogel moulded to be ~ 1 inch across and weighing 5 mg, is being balanced on the stamen of a flower).