Fusion from the fictional anime Dragon Ball Z refers to the joining to two persons to become one. This is done in a variety of ways including the Fusion Dance, body and energy merging (i.e. Namekian Fusion), and Potara Earring Fusion. Fusion in these senses is similar to Karyogamy, the joining of two cell nuclei.
Forms of Fusion
The Fusion Dance is a precise set of moves that allows two individuals to join together. Both individuals must be roughly the same size, and have the same power level at the time of fusion. If any mistakes are done during the Fusion Dance, it will either not work right or not work at all. This fusion creates a new body that resembles both characters that fused, but can have a dominant side both visually and in how they act. Its limitations are that it uses a lot of energy, and lasts no more than half an hour.
In the Dragon Ball Z manga (In the middle of Kid Buu Saga), Vegeta refuses to fuse with Goku using this method, as he consideres the dance "disgusting".
Potara Earring Fusion
The Potara fusion earrings allow for a fusion that is similar to that from the Fusion Dance, but is much more permanent as it usually can not be undone. This fusion creates a new body that resembles both characters that fused, but can have a dominant side both visually and in how they act. One property of the Potara Earing Fusion is that once the person is at a certain energy level, they can't "power down" so to speak, and so getting to a high power level could potentially shorten the character's life.
This is done by the Namek people, and allows them to join their energies and bodies together. Usually the strongest or healthiest body acts as the host for the two entities. After this is performed then the effects become Permanent but the Namek who uses this technique will inherit the other Nameks Power and Memories.
Absorption is a bit different than Fusion, as it usually involves the consumption of an individual, as opposed to a sharing of power. This is done by Cell and Buu.
List of Fusions