Question
What causes sticky stuff on the undersides of leaves of a Dracaena plant? What can I do about it? I like a natural solution. I do not like to uses pesticides. Thanks, Jane

Answer
It sounds like your plant has a problem with some type of insect.  Dracenas are often troubled by scales which will be most prevalent on the undersides of the leaves.  The scales "suck" on the sap of the plant and produce a substance called honeydew which is very sticky.  This is most likely what you have noticed on the plant.

I would start simply by washing the leaves with a clean sponge.  In about a gallon of water, I would add one or two drops of dish soap and mix.  Dip the sponge in the water and wash the plant with the sponge.  Take particular care to gently rub the underside of the leaves, especially if you see any brown bumps (these are the scales).  After your washing is complete, rinse the plant to remove excess soap.  I would wait a day or so and then treat with a homemade solution (see bloew).  

There are many home remedies for scales and other sucking insects.  You can find the recipes on the internet and they usually consist of common household products such as oil or soap.  I have pasted a few links below for recipes you can try.  I have not used these myself so I would use caution before applying the solution.  I would try the product on one or two leaves to make sure that phytotoxicity (burning) does not occur.  In trying to help your plant, you could do it more harm.
http://www.carbon-footprint-defined.com/homemade-pesticide-recipe.html
http://www.livingwithbugs.com/insecticidal_soap.html
http://www.gardeningknowhow.com/problems/scale-bug-how-to-control-plant-scale.ht...

Good luck with your plant!