Sticky residue on plant foliage can come from the feeding of any number of insects with piercing-sucking mouthparts. Aphids, scale, and mealybugs are common culprits. If the stickiness is associated with waxy white blobs, your plant has mealybugs. These insects look like little tufts of white cotton and attach themselves to plant stems, the undersides of leaves, and the places where leaves join the main stem. They pierce the plants and suck the juices. It's undigested sugar secreted by the insects that creates the sticky residue (honeydew). The honeydew can in turn allow fungus to grow. 

 

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To get rid of mealybugs, wash off the plant with a spray of soapy water. If the plant is small enough, carry it to a large sink or an outdoor area. Use insecticidal soap or a solution of dish detergent. Soak the top and bottom of all the leaves, and physically -- with the spray of water or with your fingers -- remove every cottony mass that you can see. A dab of rubbing alcohol on the cottony tuft will kill the mealybug.

Or you could apply a houseplant pesticide that's labeled effective against mealybugs. Look for a product at your local garden center. Take a leaf with you that shows the critters (carry it in a sealed, clear plastic bag) to confirm this diagnosis. Follow the directions on the pesticide carefully. You'll need to make follow-up applications at 7-10-day intervals to kill young, newly hatched mealybugs. This pest is beatable, so don't give up. If the plant is heavily infested, you can always cut off some of the most affected parts.