Dioscorides reported that ancient Greek shepherds would use the barbed stems of cleavers to make a "rough sieve", which could be used to strain milk. Carl Linnaeus later reported the same usage in Sweden, a tradition that is still practiced in modern times.
The seeds, lightly roasted, are said to make a caffeine free coffee substitute. Merritt Fernald (Ref. #6) wrote European writers are agreed that the seeds of Cleavers make the best substitute for coffee in our northern flora. When dried and slightly roasted the seeds have the flavor or aroma of coffee. This fact is of special interest since the genus Galium belongs to the same natural family [the Rubiaceae] as true coffee."
Cleavers are in the Rubiaceae family which consists of flowering plants in the coffee, madder, or bedstraw family. In particular cleavers are in the bedstraw family. There are upwards of 3,000 species in the Rubiaceae family. Other names that cleavers are known as include sticky willy, stickybud, stickyweed, kisses, and clivers.