Generally speaking, a hernia (see also
http://wiki.medpedia.com/Hernia ) is a protrusion out of a contained area through an abnormal opening. Technically, any normal barrier can have a hernia. The terminology can be a bit confusing; some people refer to the bulge that is created as the hernia, while others refer to the opening itself as the hernia. For the sake of this answer, I'll call the opening the "hernia defect" and the protruding tissue as the "hernia contents". In either case, the contents are said to "herniate" through the defect.
As I mentioned, therefore, any normal barrier can have a defect. Many of these are rare and have obscure names, you might review the (still incomplete) list of hernias at
http://en.wikipedia.org/wiki/Hernia .
The most common defects most people think of as "hernias" are in the groin region, in the area where the legs meet the pelvis. The tissue along this line is partly made up by the inguinal ligament, and defects in this tissue are called inguinal hernias (
http://wiki.medpedia.com/Inguinal_Hernia ). These may further be divided into indirect or direct inguinal hernias, depending on where exactly the defect is, but they appear similar from the outside. The hernia contents here are most commonly fat from inside the abdomen or intestine.
In the same region, a defect beneath the inguinal ligament may form a femoral hernia, and has similar contents. It may even be confused for an inguinal hernia. Obturator hernias are nearby, just behind this area in the pelvis, but are much less common and often are not detectable externally.
Moving up the abdomen, we often consider the group of hernias with defects in the abdominal muscles and thick tissues as simply "abdominal wall hernias", which again often contain fat or intestine. These may be due to a weakness in the abdominal wall (such as an "umbilical hernia"), an incision from surgery (an "incisional hernia"), or even a trauma which tears or cuts the wall.
Between the abdomen and the chest is the diaphragm (
http://wiki.medpedia.com/Diaphragm ), and diaphragmatic hernias are also described, the most common being the hiatal hernia, the herniation of the stomach (or other abdominal tissue) through the diaphragmatic hiatus, the area where the esophagus comes through the diaphragm.
As I mentioned, this is far from a complete list, but includes the most common types.