Should "I" (first person pronoun) always be used in uppercase, or does it depend on situation (uppercase in the first word of a sentence)?
And why are other pronouns not capitalized?
Yes, in standard written English, we always capitalize I.
From a Wikipedia page,
I (and only this form of the pronoun) is the only pronoun that is always capitalized. The practice became established in the late 15th century, though lowercase 'i' was sometimes found as late as the 17th century.
Additional information (to the question "Why are other pronouns not capitalized?"):
One thing that makes I unique is that I is the only one-letter pronoun. All other pronouns (including me, my, and mine) have two or more letters.
(Special thanks go to GoDucks for the link to the article Me, Myself and I.)
Yes, I (the pronoun) should always be capitalised.
A lowercase i means the letter "i" or Roman numeral 1. The only time a lower case pronoun I is acceptable is if done for reasons of style, for instance deliberately avoiding the use of all capital letters, such as alice, bob and i (normally Alice, Bob and I). I have read a published book written entirely this way, however, in mainstream writing this is usually frowned upon.
As to why the other pronouns are not capitalised, language doesn't have to have logical rules. In Latin the first letter of a sentence is not capitalised unless it is a proper noun. In German all nouns (not just proper nouns) are capitalised. English is no more or less logical than any other natural language, it's just different. The rules are somewhat arbitrary and sometimes we have evidence as to why it is the way it is and sometimes we don't.
I try to avoid mentioning other people answers, but in this case you already have some excellent links which I won't attempt to duplicate. I will, however, recommend the following entries on Wiktionary: