Ionic Bonds: Typically formed between metals and non-metals.
DNA contains a phosphate backbone. Phosphate is made up of phosphorus and oxygen atoms. The DNA molecule is also complexed with histone proteins. These non-specific interactions are formed through basic residues in the histones making ionic bonds to the acidic sugar-phosphate backbone of the DNA.
Hydrogen Bonds: The DNA double helix is stabilized by hydrogen bonds between the bases attached to the two strands. The four bases found in DNA are adenine (abbreviated A), cytosine (C), guanine (G) and thymine (T). Each type of base on one strand forms a bond with just one type of base on the other strand. This is called complementary base pairing. Here, purines form hydrogen bonds to pyrimidines, with A bonding only to T, and C bonding only to G. This arrangement of two nucleotides binding together across the double helix is called a base pair [See attachment].
Hydrophobic Interactions: The face of each
base (as opposed to the edges) is hydrophobic and the bases are protected from interaction with water by the structure of the double helix.
Van der Waals Interactions found in DNA
base stacking: When ring structures such as those found in nucleotide bases are stacked flat against each other, they experience small forces of attraction. This is called base stacking, and though the individual forces are weak, like hydrogen bonds they become a major factor when you add them over several thousand base pairs.
For more information:
http://higheredbcs.wiley.com/legacy/college/boyer/0471661791/structure/dna/dna.htm