Because the sensation of falling is understood to be part of the body's physiological response to drifting off to sleep, it's perhaps no surprise that the feeling so commonly shows up in our dreams. Whether you dream about frequent tripping, having trouble standing up, or falling off a cliff, the symbolic meaning is likely the same: typically, a kind of loss, whether material or figurative. You may be going through lowered self-esteem, a job loss, or a strained relationship. In other cases, the fall might be more representative of a leap away from something you fear, whether temptation or conflicted feelings.
Flying, pretty typically, represents a symbolic freedom from one's physical body or earthly restraints. Usually, flying in dreams is a pleasant experience, reflective of the fact that you're feeling good about something in your waking life: maybe it's a new relationship, or recent graduation, or another promising development. Occasionally, you may dream that you are trying to fly, but remain tethered to the ground in some way; usually this means that you're meeting resistance in something you want to do, or are hesitant because of a fear of failure.
For how weird dreaming about teeth (particularly losing them) may seem, it's one of the most common dream themes there is — perhaps because it's generally thought to represent anxiety. (A feeling that may manifest in more literal ways too, perhaps through nighttime teeth grinding.) Often this anxiety is generalized or unaddressed, though some interpreters suggest dreaming of lost/ruined teeth may reflect insecurity with one's appearance. Still more literal interpreters have said that dreaming of teeth means that you need to go to the dentist, which is probably always a good idea anyway.
Dreaming of our hair is, unsurprisingly, thought to be indicative of our self-image, and sometimes sexuality. Large quantities of attractive, healthy hair is thought to be a symbol of virility, while dreaming of, say, picking one's split ends or cutting one's hair off completely may reveal insecurities about one's appearance, or a decreased libido.
5. The ocean
Water in dreams is thought to represent the unconscious mind, or something that's been bubbling to the surface of your brain but has not yet become fully clear. If you're on a shore overlooking a calm, beautiful ocean, that's likely to mean that whatever's been on your (subconscious) mind is something that will bring you peace and resolve. If, however, you're dreaming of turbulent seas, it could mean that you're ignoring something, or trying to suppress something you may, on a deeper level, already know to be true.
6. Being naked
The symbolic meaning of nudity in one's dreams is often context-specific: when it's unintentional, and especially when it's suddenly revealed to you as a surprise (as in the case of dreaming about going to school and only realizing halfway through class that you forgot to put on pants), it often indicates vulnerability and/or feelings of inadequacy. It's telling if the people around you in the dream don't notice — this usually suggests that your concerns are exaggerated, or obvious only to you. And if you're showing off your naked self in your dreams, it might indicate fairly literal sexual urges, or it might just mean you have an unmet desire to be recognized for something.
Dreaming about sex is often not thought to be very symbolic at all. Often it just means you want to have sex. It is, perhaps, your brain's way of telling you that you are DTF. However, some interpreters believe that dreaming of sex can be more representative of an unprecedented unity between conscious and subconscious, or the arrival of new opportunities for personal growth.
8. Things that don't work
This category can be a little nebulous, but dreaming of things that don't work — like computer screens you can't read, or fuzzy TVs, or a treadmill that won't go the speed you want it to — are thought to be indicative of the brain's language centers shutting down while asleep. You may feel that you are unable to communicate in the way you'd like. You might be frustrated or stalled in a project, or be suffering from performance anxiety of some kind.
Dreaming of an exam (or a class, typically one for which you are vastly unprepared) is another common theme that can represent a variety of anxieties. If you are currently a student, you probably know the reason for this. Go study! If you're not currently a student, dreaming of an exam often represents anxiety about a recent or upcoming change. Exams are also, relatedly, representative of the end of something, and dreaming about them suggests that while you may be nervous about it, you have gone through what you needed to go through in order to move forward.