Question
my globe willows are approx. 5 years old and during the summer the leaves are sticky and shiny and when you stand under the branches it feels like its raining. is there a problem?

Answer
Sounds like either an insect called an aphid or a scale insect. Both suck the plant juice from the foliage and twigs and secrete a substance called honeydew which is high in sugar content and sticky. Control the sucking insects and the sap will stop dripping.

On small trees I would spray the foliage with an insecticide called Orthene. You will need top cover all the foliage with the spray.
Next spring I would treat the tree with a soil applied insecticide--this will last the whole season. Since it is getting into Fall soon the soil applied wil not work as well now since the tree soon will stop growing for the winter.
Apply an insecticide to the soil around the tree. Treat with  an insecticide called Bayer Advanced Tree and Shrub Insect control. The root swill absorb the insecticide and transport it to the foliage and when the insect suck the plant juice they are killed. Check with your local nursery for these insecticides. Here is a web link to more information on this product.  

http://www.bayeradvanced.com/tree-shrub-care/products/12-month-tree-shrub-insect