Why does Spanish allow the double negative?

The difference between English and Spanish...
In Spanish, "no tengo nada" means "I have nothing" or "I don't have anything".  It does not mean "I don't have nothing".  This is often confusing for those who speak English, in which two negatives cancel each other out and make a positive.  In Spanish, on the other hand, adding a negative can reinforce the negativity of the phrase, not eliminate it.  For example, the negativity in the phrase "no lo haré nunca" sounds stronger than it does in "no lo haré" or "nunca lo haré".  


When is it acceptable/necessary to use a double negative in Spanish?
There are two types of negatives in Spanish...
Type 1: no  
Type 2: nunca, jamás, tampoco, nadie, nada, ninguno, ni.  


You can combine "no" with any of the Type 2 words in order to make a double negative.  The best way to explain how to do this is by example:

"No voy al teatro" - correct
"Nunca voy al teatro" - correct
"Voy nunca al teatro" - incorrect
"No voy nunca al teatro" - correct

If a Type 2 negative goes before the verb, there is no reason to include "no".  If it goes after the verb, you must put "no" before the verb.