[CliffordK (OP)]

Why does one take some medication under the tongue?

Aspirin.
nitroglycerin.

Would it be just as good to take it on the tongue?
Is it all about taste?
Does one swallow less of it when it is held below the tongue rather than on the tongue?

[cheryl j]

I think there are thin walled capillaries under the tongue that the medication can pass through more quickly than if it is swallowed and has to be absorbed through the walls and capillaries in the stomach and/or small intestines. If it goes right into the blood stream under the tongue, it also by passes the liver (for a while) which will naturally break down and decrease the dose.  Whether a medication can get into the body this way probably depends on the size of the molecule of the drug. 

[Lmnre]

With nitroglycerine, it's a matter of quick absorption to relieve an ongoing heart attack as soon as possible and to bypass the digestive system, which would take too much time and would destroy it, which would make it useless. 

The digestive system would digest nitroglycerine. Enduring the rigors of digestion is also why some protein-based medicines (such as insulin) are injected, otherwise they would be digested (ie, reduced to its parts) and, thus, rendered useless.

The "A" in the term "ADME" stands for Absorption.