I speak three languages. Two of them make use of the familiar first person pronoun. Spanish uses “tu”, Maya uses “tech”. Old English used “thee”. For you that know of other languages, or you that study linguistics, is the familiar used?
Japanese experts can check me on this, but I believe kisama is the familiar second person singular and kimi is the formal.
French has toi as informal and vous as formal. Catalan has tu and vosté/vos (varies by dialect).
German has du and sie.
Finnish has familiar “sinä” and formal “te”, but the latter is rarely used except by shop attendants and the like.
I think it’s actually du and Sie. sie is “she.”
The Wikipedia article on Japanese pronouns lists about 10 words for “you” (singular). Most range from informal to extremely rude, and the only one with a formal register in common use is “otaku”, which usually means something else (as it does in English).
Japanese people avoid using words for “you”, with the exception of “anata” which is used by married women to address their husbands (and so is informal). Unless you are being rude, when you are referring to the person you are addressing, you use their name with an appropriate honorific, or you leave the name out altogether if it obvious who you are referring to from the context.
Lower case “sie” is both “she” and “they”.
Dutch:
jij/je - familiar (it’s not a gender distinction, more a question of emphasis)
(gij/ge - archaic familiar, still in use in Belgium cos them people talk funneh)
u - formal
Portuguese:
tu - familiar
você - formal
o senhor/a senhora - more formal, literally meaning “the gentleman/the lady”, but used as personal pronoun, so eg “a senhora vai sozinha?” = lit. “the lady is going alone?”, but means “are you going alone?”
In Brazil an interesting thing is happening at the moment, really the same thing that has already happened in English: as “tu” has fallen into disuse, it is becoming archaic. As it becomes archaic, it seems formal to uneducated people, even though it originally isn’t formal. It sounds like the language of the bible to people who don’t otherwise use it, or like Shakespeare. So it is becoming like “thee” in English: it’s familiar, but many people mistake it for being formal purely because it’s archaic. The best thing is, they don’t know how to conjugate the verbs to go with “tu”, so they will use the conjugation for você: eg “tu vai”, when it should be “tu vais” or “você vai”.
Romanian:
tu - familiar
dumneata - medium familiar, eg an older person addressing a younger person they don’t know
dumneavoastră - formal (I love this one, how awesome is that word?!)
That’s funny. My daughter says, “Tell them to go back before they have to invent ‘y’all’!”
The Spanish that’s spoken in New Mexico seems to be going the opposite direction: “tu” is used almost exclusively nowadays, and when I’ve used my laughably primitive high-school Spanish on actual Spanish-speakers, I can see them stifling hilarity as I “usted” them all over the place to show respect.
Russian ty (informal) and vy (formal), ты and вы in Cyrillic.
I believe the same is true for every other Slavic language I’ve encountered (Czech, Slovak, Polish, Belarussian, Ukrainian).
Swedish is similar. Du/dig is the familiar and ni/er is the formal, but the formal has fallen out of usage and instead is only really used as the plural these days.
Italian: tu and voi are informal; Lei and Loro are formal.
Haha! It’s ok, they’re safe as they already have a grammatically correct form of y’all: vocês.
Reminds me of a production of A Midsummer Night’s Dream I was in years ago. There was a girl from Texas who just couldn’t stop herself from saying “th’all”. Brilliant! 
Vietnamese has a crazy number of pronouns that differ by gender, familiarity, social status, familial relationship and any number of other factors. The system of familial pronouns (big sister, little sibling, aunt, etc) does double duty to refer to certain other non-relatives in various settings.
But short answer is yes, degree of familiarity does change the pronoun used.
Turkish has sen (informal) and *siz *(formal/plural).
OP, are you asking familiar / formal or singular / plural? The latter is very common in world languages, probably the default, while the former is rarer.
The English singular / informal was thou; thee is the object case, like I and me.
Irish has singular / plural, but as far as I understand the plural (sibh) isn’t used as a formal; that’s still the singular tú. Scottish Gaelic, on the other hand, uses sibh as a formal. Welsh and Breton also do the plural = formal thing. Welsh singular/informal is ti (S. Wales) / chdi (parts of N. Wales, some constructions), plural chi; Breton is te and c’hwi.
The German and Italian formals, on the other hand, appear to come from the third person. I am not sure about the German, but in Italian you use the 3rd person verb. You do in Spanish as well, but Usted comes from vuestra merced, “your (pl.) mercy”.
In Mandarin, “ni” is informal and “nin” is “formal”, or honorific, I should say. Hardly ever used in the diaspora, I think, but you would have to get a mainlander to confirm if it’s used commonly there.
What amanset wrote with the addition that Swedish shop assistants are like the Finnish ones and say Ni, thinking they are polite, when they really are frightfully insulting to us oldies who know that Ni is the old way to address underlings and were very happy when the use of du broke through and spared us from a number of awkward ways to address people we weren’t familiar with.
Seriously? I didn’t actually know that. At this rate “ni” must be due a change of meaning again soon