We have no idea about the frequency of suicide in prehistoric times. I think it is a human phenomenon, so it will have occurred. But we have no chance to generate valid data about it.
In Ancient Egypt the suicide was seen as a kind of sin against oneself. We know a numer of examples of that.
The best known of all is the "Dialogue of a Man with his ba/soul", where, given a desperate situation, the main character of the text thinks about the suicide as the end of his problems. About this text there exists one book very recently published, whose author is James P. Allen. Also, an article by C. Barbotin in the last issue of "Revue d'Égyptologie" gathers a lot of information of it and a new interpretation.
You can also gather some information in the "Book of the Dead". Also a very important document are the Judicial Papyri of the end of the New Kingdom (see e. g. P. Vernus, "Affairs and Scandals in Ancient Egypt"). There, on those acts the condemned persons where re-named, and also forced to kill themselves.
I hope this can help you. If you need more information about this question, please make me know.
Francisco, could you send me some info on suicide in Ancient Egypt? One of the sources I gave Tarun opens with this statement: "To the ancient Egyptians, suicide was not a violation of either the spiritual or legal code."
I realize the sources I provided were weak at best, but I just sent what I found after a quick search, hoping to at least help Tarun get started. But if you're correct than it seems what I found is wrong so I would like to read the correct text.
What Minois, Durkheim, and Murray suggest is that suicide is largely a modern social construct. Applying a quite broad, etic definition means that we can assume some suicide was found in the ancient world and certainly Chinese texts suggest that honor-killings or going on "suicide-missions" was a reality.
This seems to intensitfy with increasing social complexity, population-size and (I'd posit) inequality, like slavery. In terms of documenting this without written-texts or iconography, it'd be difficult to identify skeletal correlates that aren't also quite suggestive of other kinds of violence (see chapters in Martin and Anderson's Bioarchaeological and Forensic Perspectives on Violence, Cambridge University Press [2014]; particularly chapters by Crandall et al. and Stefan for examples of how troubling distinguishing cause of death from remains can be). Overall, we'd assume that it is a lower prevalence because there are numerous mechanisms of ancient social control.
It'd be worth an examination of HRAF to see if ethnographic studies of small-scale and middle-range societies yields evidence of suicide though I suspect this is mocked through social performances and rituals which help integrate individuals and provide social support.