This is a very interesting question. Glycerol is sticky based on two characteristics: Its viscosity, and its hydrophillic/hydrophobic tendencies. First, I'll describe more about viscosity.
Viscosity is the 'thickness' of matter. For example, oil that you place in your car is relatively thin (can be poured and not easily scooped), while grease is relatively thick (must be scooped and cannot be poured). When no coating exists (when placing your fingers together in a 'snapping' motion), your fingers will eventually get warm due to the high friction. If you placed oil between your snapping fingers on one hand and grease on the other hand, and snapped your fingers for a long time, it would take signifacently longer for the grease to wear off of your fingers than the grease. Glycerol is more viscous than water and tends to keep the coating tenatious.
Glycerol is one of those wonderful chemicals that are used for many things because they can attract oil or water. The coating mentioned above must attach temporarily to create this 'stickiness tendency'. Hydrophillic chemicals coat readily with water, hydrophobic compounds readily coat with hydrocarbons. Since glycerol is both hydrophobic and hydrophillic it will readily coat with either of these two chemical types.
Since glycerol is both viscous and can attach with almost any compound due to its hydrophillic/hydrophobic tendencies, it is 'sticky' to almost everything.
I hope this helps,
Eugene Dakin Ph.D., P.Chem.