What are the rules for capitalization?

The rules of capitalization are quite extensive and depend somewhat on the context in which the words are used. The basic rules are to capitalize:

The first word of a sentence
Names of the days of the week, months of the year
The pronoun I
Names, including initials, of individuals
Titles which precede names
All names of holidays (excluding any prepositions)
The first word and all nouns in a salutation
The first word in the complimentary closing of a letter
Family relationship names when they precede a name or are used in place of person's name, especially in direct address
All words in the names of specific organizations and agencies excluding prepositions, conjunctions, and articles
Names of languages
Names of definite sections of a country or the world
Names of nationalities
Names of religions and deities
Adjectives formed from names of geographical locations, languages, races, nationalities, and religions
The first word and all the words in titles of books, articles, works of art, etc., excluding short prepositions, conjunctions, and articles