Many things can happen, and it's hard to be exhaustive when the stories are so subjective and not a lot of research can be done on psychedelics yet.
First, for some people, psychedelics can trigger things they were not aware of (but likely in their family history or personal history) such as schizophrenia or episodes of past trauma. This is not really the norm, but is sometimes not mentioned by people who are afraid of the "demonization" of those drugs.
Depending on the dose, the drug, and the susceptibility of the person, one can also experience gaps in memory which create confusion in the moment (and in some cases after the trip), or a psychotic state (which can end up being manageable with knowledge and support for some, and a trip to sleep through the night in a hospital for others).
If we're not talking about these things, then bad trips can have physical components as well as psychological ones. For example: seeing horrific visions (when closing your eyes most often, sometimes even with eyes open), having a "body feeling" that just doesn't feel quite right (messed up proprioception, nausea), having thought patterns that take you down a negative spiral..
Examples of horrific visions: fractals of upsetting images that may or may not be related to experiences you've had (from past traumas to movies, or even random bits of your perception you weren't quite aware of).
Examples of body feeling issues: feeling like parts of the body aren't where they are ("my nose is a few centimeters off"), speech impediment/slurring, losing control of limbs temporarily (which can create a lot of fear and confusion)
Examples of thought patterns that create panic/anxiety/fear: thinking that the current state will last forever (forgetting that the psychedelic effect will wear off), feeling a lot of emotions without understanding the specific cause, perceiving some past trauma and not being resilient against it, heightened empathy being overwhelming, forgetting that perceptions are altered which affects behaviour ("I can't walk this path because it's too steep" on a flat path).
There's so much more to say about that, and also so much to say about proper preparation (set, setting, support) which can prevent almost all the problems listed, but it's important to remember that psychedelics are not a joke. Particularly so when getting into high doses, "research chemicals", or simply powerful ones (DMT comes to mind for intensity, or STP/DOM for length)