Non-blunt ends are created by various overhangs. An overhang is a stretch of unpaired nucleotides in the end of a DNA molecule. These unpaired nucleotides can be in either strand, creating either 3 or 5 overhangs. These overhangs are in most cases palindromic.
The simplest case of an overhang is a single nucleotide. This is most often adenine and is created as a 3 overhang by some DNA polymerases. Most commonly this is used in cloning PCR products created by such an enzyme. The product is joined with a linear DNA molecule with a 3 thymine overhang. Since adenine and thymine form a base pair, this facilitates the joining of the two molecules by a ligase, yielding a circular molecule. Here is an example of an A-overhang:
Longer overhangs are called cohesive ends or sticky ends. They are most often created by restriction endonucleases when they cut DNA. Very often they cut the two DNA strands four base pairs from each other, creating a four-base 3 overhang in one molecule and a complementary 3 overhang in the other. These ends are called cohesive since they are easily joined back together by a ligase.
For example, these two "sticky" ends are compatible:
Also, since different restriction endonucleases usually create different overhangs, it is possible to create a plasmid by excising a piece of DNA (using a different enzyme for each end) and then joining it to another DNA molecule with ends trimmed by the same enzymes. Since the overhangs have to be complementary in order for the ligase to work, the two molecules can only join in one orientation. This is often highly desirable in molecular biology.