Precipitant, precipitate, precipitous: All three come from the same root, the Latin praecipitare ("to throw headlong"). Precipitous means steep, like a cliff. It should no be used, as it often is, to describe actions (e.g. "precipitous departure"), as it can only describe physical characteristics. Precipitant and precipitate both indicate a headlong rush and are almost indistinguishable, but the first tends to emphasize abruptness, and the second rashness.
Precondition, preplanning, prerecorded, etc. Almost always redundant; "pre-" adds nothing and should be deleted.
Prescribe, proscribe. The first means to set down as a rule or guide; the second means to denounce or prohibit. If you get bronchitis your doctor may prescribe antibiotics and proscribe smoking.
Pristine. Does not mean simply sparkling or tidy, but pure and unchanged from an original condition.
Prodigal. Does not mean wandering or given to running away, a sense often wrongly inferred from the biblical story of the prodigal son; It means recklessly wasteful or extravagant.
Prone, prostrate, recumbent, supine. Supine means lying face upward. Most, but not all, agree that prone and prostrate mean lying face downward (a few say it can also mean face-up). Prostrate should mean throwing oneself down, in submission or for protection, and should not be used to describe someone sleeping, for example. Recumbent means lying flat in any position and indicates ease and comfort.
Prototype is a word for an original that serves as a model for later products of its type. Most qualifying descriptions -- first prototype, experimental prototype, and so on -- are redundant.