What are the different kinds of bites?

The technical term for a bite, or the way the teeth fit together, is "occlusion," with the term "malocclusion" meaning that the teeth are misaligned (or, literally, "bad bite.")

There are three main types of malocclusions that may be treated by orthodontics or a combination of orthodontics and jaw surgery (adults) or orthodontics and growth modification (children).

Class I: The upper and lower jaw are correctly aligned, but there may be problems with spacing, crowding, crooked teeth, or over or under eruption (teeth are growing above the gumline, above other teeth, for example.) These problems can usually be fixed with orthodontics.

Class II: This is otherwise known as an overjet, which means the upper teeth are quite a bit more forward than the lower teeth. In cases where there is only a slight overbite, it may be treated with orthodontics; however, in cases where the overbite is significant, growth modification (children) or jaw surgery to move the upper jaw backward and/or the lower jaw forward (adults) may be required in addition to orthodontics.

Class III: This bite is often called an underbite or a negative overjet. In this case, the lower teeth sit in front of the upper teeth. This issue may sometimes be treated with orthodontics alone, if it is a slight underbite, but if the distance between the upper and lower teeth is significant, growth modification (children) or jaw surgery to move the lower jaw backward and/or the upper jaw forward (adults) may be required in addition to orthodontics.

The above three bites have to do with the horizontal plane of the mouth (forward or backward.) There are two bites that have to do with the vertical plane (up or down):

Open bite: People who have this kind of bite often have "long faces." When those with open bites try to close their teeth together, only a few teeth meet, usually at the back of the mouth. You can actually see the inside of the person's mouth while s/he is biting down with an open bite. This type of bite cannot be treated with orthodontics alone, as it is caused by a jaw abnormality and requires upper jaw surgery (adults and some children) along with orthodontics.

Deep bite: This is when the upper teeth overlap the bottom teeth vertically. In other words, very little of the lower teeth can be seen when the person bites down. This is sometimes called an overbite, though some people may use the term "overbite" to refer to Class II malocclusions as well.
A deep bite is also a jaw abnormality that cannot be treated with orthodontics alone, and requires orthodontics and growth modification (children) or orthodontics and upper jaw surgery (adults).

The final type of bite has to do with the horizontal plane, but side-to-side rather than forward or backward (as with the Class I, II and III bites):

Crossbite: This occurs when the bottom teeth don't meet up correctly with the top teeth on the sides of the mouth. When the upper teeth fall inside the lower teeth on one side of the mouth, it's called a unilateral posterior crossbite. When it happens on both sides of the mouth, it is known as a bilateral posterior crossbite. (A Class III malocclusion (underbite) is also called an anterior crossbite.) A crossbite may be caused by the upper jaw being too wide or too narrow for the lower jaw, requiring orthodontics and growth modification (children) or orthodontics and jaw surgery (adults) to correct.