Asyndeton and Polysyndeton are plays on grammar. Asyndeton means "without conjunction" and polysyndeton means "many conjunctions."
Asyndeton
A scheme in which a conjunction that would be expected grammatically is absent.
Polysyndeton
A scheme in which more conjunctions are used than are required grammatically.
Examples
A sentence from Kennedy's Berlin Wall Address includes both asyndeton and polysyndeton in succeeding clauses:
"I know of no town, no city, that has been besieged for 18 years that still lives with the vitality and the force, and the hope and the determination of the city of West Berlin."
In the opening clause, there is a lack of conjunction between "no town [and/nor] no city". In the last clause, "vitality, force, hope and determination" are each set off with separate conjunctions.