Why do we add salt when precipitating DNA? All the DNA extraction protocols I have seen involve adding salts to the extraction buffer. What is the purpose of the salts? What happens if they aren't included?

The role of the salt is to neutralize the charge of the DNA's sugar phosphate backbone. This makes the DNA less hydrophilic (less soluble in water).

Ethanol has a lower dielectric constant than water so it's used to promote ionic bonds between the Na+ (from the salt) and the PO3- (from the DNA backbone) causing the DNA to precipitate.