One is a pronoun in the English language. It is a gender-neutral, indefinite pronoun, meaning roughly "a person". For purposes of verb agreement it is a third-person singular pronoun, although it is sometimes used with first-person reference. It is more or less equivalent to the French pronoun on, the German man, and the Spanish uno.
However in American English it has quite formal connotations, and is often avoided in favor of more colloquial alternatives such as generic you. It is more common in British English where it does not have the same connotations. 
The word one as a numeral can also be put to use as a pronoun, as in one was clean and the other was dirty, and can form pronominal phrases in combination with another determiner, such as the one, this one, my one, etc. This article, however, concerns the use of one as an indefinite pronoun as described in the previous paragraph.
Cases and usage
One may be used in the nominative case, but (much unlike French on and German man) it can also be used in other cases. It occurs most commonly in sentences in the present simple tense or conditional constructions. Examples of its use:
- One cannot help but grow older.
- If one were to fail, that would be unfortunate.
- Drunkenness makes one unreliable.
- A reputation travels with one.
- That dead-end job at least gives one a chance to develop as a person.
The genitive, or possessive, form of one is one's, as in
- One's experiences shape one's expectations.
There is no strong form analogous to hers and yours:
- *One's is broken
- *I sat on one's
- *I broke one's
*This is not standard English.
A reflexive form oneself appears at times:
- To quit smoking is like giving oneself a raise.
Oneself is anomalous in its inability to refer back to anything other than one:
- One exhausts oneself.
- * A person exhausts oneself. (not valid)
All English possessive personal pronouns, such as his, hers, and its, do not contain an apostrophe, except for one.
- Example: One's apostrophes should always be placed correctly.
The reason for this anomaly is that in addition to being a personal pronoun, one also doubles as an indefinite pronoun, which does use an apostrophe in its possessive form.
- Examples: someone's, everybody's
Some people find the repetitive use of "one" to be stilted so they will use generic "he":
"One can glean from this whatever he may." OR: One can glean from this whatever one may."
"If one were to look at himself, he would see..." OR: If one were to look at oneself, one would see..."
Either form is considered to be correct in formal English, but the form with "he" is sometimes viewed as sexist. (See Gender-neutral pronoun.) To avoid this, and because the thrice repeated "one" in this case can be used to subtly imply that "one" is the listener, and that they are doing something wrong (in the above example, it would imply that the person does not look into some aspect of their own behavior, and that, if they did, they would find some flaw, usually indicated in the continuation of the sentence), the singular they is often used. For example:
"If one were to look at themself, they would see..."
Many language purists, however, consider singular they to be grammatically incorrect, and would thus discourage its use, especially in writing.
Style and rhetoric
In English, one can be considered to be overly formal, and people tend to avoid it. However, in doing so, they encounter problems only resolvable by awkward phrasings or a significant drop in formality. In particular, phrasing a sentence in a gender neutral way may require the passive voice, singular they, pluralising, you, or circumlocution. In addition, the word one can also be used for inanimate objects, creating possible confusion in careless writing. For example,
- If one chooses to disobey the rules, one must be dealt with.
The second one may co-refer with the first, or it may refer to a specific rule. (If this sentence were spoken at all, the second one would require distinctive intonation for the second interpretation.)
One may have come into use as an imitation of French on. French on derives from Latin homo, nominative singular for human, through Old French hom[me]. It is distinct from the French word for the numeral one, un(e).
- Katie Wales, "Impersonal one: a new personal pronoun", Personal pronouns in present-day English, pp. 78+