Three classifications; Artemidorus who was the classical inspiration for Jung and Freud classifies them in two camps:
Enhypnia: non predictive, and Oneiro: prophetic. We will add a third classification with the insight of Freud which we will call Psychoanalytic.
Enhypnia will be your average dream that is just an amalgamation of things that occurred during your day, Artemidorus also lists these as being anxiety motivated in that if you are worried about money you may dream about money etc etc. These dreams are mundane in nature but can provide insight into what our primary concern is amongst the noise of conscious thought.
Psychoanalytic dreams are going to be heavily symbol laden and can also be anxiety motivated, however they are often repetitive and stand out to the dreamer as profound. For example one may have a reoccurring dream that is extremely vivid of being trapped in an empty house. This dream is the subconscious mind trying to communicate with the conscious mind about some type of pressing psychological emergency and should be interpreted and dealt with according to the symbols.
Oneiros can fall in two camps, prophetic and visitation. Most occultists, psychics, and spiritualists will be familiar with these dreams. The prophetic Oneiros is considered by Artemidorus to be directly from the gods and not within, this can predict a death or traumatic event. Or if it is a massive event such as the destruction of a city will afflict multiple people within the population. Jung experienced this type of prophetic dream in regards to World War 2 as well as a plethora of his clients. Artemidorus however states that these types of prophetic dreams usually only afflict the person who has responsibility for the situation. For example, only a King will have a prophetic oneiro about his kingdom being invaded. The visitation dreams occultists are familiar with as this is when a god, spirit, or the deceased visit the dreamer to provide them with guidance. Those of us who have had them know what this feels like as the visitation is marked with a synchronicity in waking life and an extremely profound feeling upon awakening.
I usually classify dreams for myself and amongst people I interpret within these camps. A solid lucid dreaming practice helps the interpreter pick up on the subtleties of where to place the dreams.