Below is a short guide to the common types of malocclusions in dogs and sometimes cats, and the sequela if they are not treated.
Class I malocclusion: The abnormal tooth
In a class I malocclusion one or more teeth have erupted in the wrong position and the upper and lower jaw lengths are normal. There are a number of possibilities with this malocclusion. Typically, this type of malocclusion causes tooth on tooth or tooth on gingiva contact that causes pain or prevents the animal from completely closing their mouth. Overtime, besides the chronic pain the animal is feeling, it can also cause severe infection and problems for additional teeth. Below are some examples of a Class I malocclusion.
Base narrow canines:
Base narrow canine malocclusion is when the lower canine teeth erupt too far inside the mouth and hit the gingiva instead of sitting nicely between the upper canine and 3rd upper incisor. This often comes along with a class II malocclusion (overbite) which we will discuss next. This malocclusion can cause significant problems and pain as it can cause large lesions in the gingiva that can even go up into the nasal sinus if it goes on for too long. There are several things that can be done for this malocclusion and even options that save the teeth. It is easier to treat and there are more options the sooner it is diagnosed and treated.

The deciduous (baby) canines can even erupt base narrow and the sooner they are removed, the less painful the puppy will be and the better chance that the adult teeth will come in more normally. Below is a puppy with lesions on the inside of his upper canines from his lower deciduous canines hitting the gingiva. He also had retained deciduous teeth where the adult incisors were trying to come in. All of these deciduous teeth were removed to give the adult teeth every opportunity to erupt where they should without interference from the deciduous tooth occupying the space where it needed to go.

Mesioverted (Lanced) upper canines:
Mesioverted maxillary canines is a common malocclusion in Shelties where the upper canine comes in pointed more toward the front of the mouth and will often keep them from closing their mouth completely. In the case below, it also caused the lower canine to come in base narrow since it was not able to erupt between the upper canine and 3rd incisor. This can sometimes be corrected with a device to slowly move the tooth. In the example below, because the tooth was also rotated and there was a base narrow lower canine, we elected to remove the upper canine to create a space for the lower canine to occupy.

Anterior or Rostral Crossbite:
An anterior or rostral crossbite is when one or more upper incisors that have erupted inside of the lower incisors instead of being slightly outside of them. This can prevent the animal from completely closing their mouth and can lead to periodontal disease. In the example below, the left first incisor had significant dental disease and was mobile from the chronic malocclusion.

Posterior or Caudal Crossbite:
Posterior or caudal crossbite is when one or more of the upper premolars have erupted on the inside of the lower premolars or molars instead of the normal outside (buccal) position. This commonly affected the upper 4th premolar.
Class II malocclusion (Overbite):
In a class II malocclusion, the jaw length is the problem, not the individual teeth. However, the teeth are what cause the discomfort. The lower jaw has not grown proportionally to the upper jaw and so the mandible (lower jaw) is shorter than the maxilla (upper jaw). This is not considered normal in any breed but can happen in some breeds more than others such as the German Shepard.
A problem occurs when the lower incisors and canines are contacting the upper gingiva causing indentations/trauma and constant pain. This malocclusion is evident when the animal is very young and can be addressed early with the deciduous (baby) teeth to try and give the lower jaw every opportunity to grow forward and to prevent constant pain in the puppy.
In the puppy below, the mandible was just slightly shorter than the maxilla but enough that it caused the lower canines to cause significant trauma to the gingiva inside the upper canines. The lower deciduous canine and incisors were all removed so that nothing was hitting the gingiva to prevent pain but also to give the mandible every chance to grow to the same length as the maxilla. The puppy will be rechecked around 5 months to see how the adult teeth are erupting and if anything more needs to be done for the adult teeth. This can be treated as early as 6-8 weeks of age to give the mandible as much time to grow as possible and to reduce pain.
Class III Malocclusion (Underbite):
A class III malocclusion is when the maxilla (upper jaw) is shorter than the mandible (upper jaw). This is the most common form of malocclusion and is even considered normal for some breeds such as the Boxer. However, just because it is considered breed standard, does not mean that it does not need to be addressed if it is causing a problem.
The most common problem that occurs with this malocclusion is that the upper incisors hit the gingiva behind the lower incisors and inside the lower canines. This causes chronic pain and eventually disease of the lower incisors and canines.
In the example below, significant trauma occurred to the lower incisors from the chronic traumatic malocclusion. The lower incisors were loose and non-vital. One of the lower canines was pushed outward by the upper incisors and the other canine had a large pocket on the inside of it. Thankfully both lower canines were savable but the lower incisors were removed along with the upper incisors causing the problem.
Class IV Malocclusion: Length of jaw is not the same side to side
The final class of malocclusion, class IV, is when one side of the mandible or maxilla or both is not the same length as the other side. This is the least common malocclusion of the four. Again, this may or may not be a problem for the animal depending on where the teeth erupt.
Below is an example of a common Class IV malocclusion called a wry bite. The incisors are not level in this malocclusion due to the mandible and/or maxilla being longer on one side than the other.

Early Diagnosis and Treatment is Key
The take away message here is that malocclusion are not only common in dogs and cats, but they also commonly need treatment to prevent chronic pain, infection, and disease of other teeth. Also, just because a malocclusion may be considered breed standard for the animal, that does not mean it does not need to be addressed. Finally, the earlier these problems are diagnosed and treated, the more options that are for treatment that often can include saving teeth, and the less pain the pet will experience. The occlusion on all pets should be checked frequently early on and throughout its lifetime to ensure a comfortable, healthy mouth.