I don’t think there’s a clear general rule for that. Dutch ‘u’ (formal) vs ‘je/jij’ (informal) don’t seem to be related to anything current. The “majestic plural” may have more clear roots, though.
Mostly, its the second person plural that is used (this true for the Slavic and the Romance languages). As you note, in German, it’s the 3rd person plural. Intriguingly (I find, at least), this form also exists in archaic (19th century) Czech in addition to the 2nd person plural.
Dutch is something of a mixed bag. It tends to follow the 3rd person singular, which means adding a -t to the stem of the verb. However, in the case of irregular verbs (to be, to want, to will, to can), this usage has shifted towards the second person singular. Other than regular 2nd person singular, however, the formal form does not drop the -t in sentences that are questions. Compare:
jij bent; ben jij? - you (sg. informal) are; are you (sg. informal)?
hij is; is hij? - he is; is he?
u bent, bent u? - you (fml) are? are you (fml)?
In older (pre WWII, I guess, if not older), you would find *u is; *is u? instead.
With Japanese there are several different ways to say the equivalent of “I” and “you” ranging from very formal to insulting. Interestingly, some of the more casual/insulting ones came from older forms of polite address, like お宅 or お前 that eventually became sarcastic. Like saying, “sir” but using the same tone of voice that you’d use for “cur.”
Besides the pronouns, there are different verb endings for casual and polite speech, while honorific speech has some specialized grammar and vocabulary.
Using too-polite forms of address can get you in almost as much trouble as too-casual ones since it can be interpreted as being either deliberately sarcastic or extremely bad at reading social cues. The default ~masu level and limited forms of address that they usually teach in school are unlikely to cause problems, but unless you pick up or learn the other registers, you’ll eventually be inadvertently damaging or limiting your relationships with Japanese people. Formal speech around people you want to be friends with is going to make them think you’re cold, and lack of proper honorifics in business can possibly cost you and your company.
You have to learn to think in a slightly different way about inter-personal and inter-group relationships, and you also have to be alert for social cues. The same person in one situation might be okay to bullshit with using informal forms, but in another situation you might have to use 敬語 to show respect. You generally get used to it after a while, but I do find it to be a pain in the ass sometimes.
For native speakers, I think it pretty much comes naturally. In Korea we have “nuh” which is the most informal way of saying you. I’d never use it unless I’m with someone I’m very familiar with who is also younger than me or the same age. We also have “dang-shin” which is more formal but in some ways more intimate since it’s usually used between adults who are also friends (children would not use this form, nor would anyone address a child this way). It gets confusing because dang-shin can also be used as a third-person way to address someone higher than you. Then there’s the word “ja-gi” which can be used as an endearment like “honey” but is also commonly used between co-workers who are equal, or used by a higher person to a lower person.
When it comes right down to it, though, the second person is considered generally less formal than the third person, so in any situation that demands formality you would use a third-person title rather than a second-person. (For example, my little brother would never address me in the second person - he has to call me nu-na, which means big sister if the speaker is male.)
I’ve been in Germany for 8 years now and I still have problems sometimes.
I still forget to pay attention during conversations to see how the other party addresses me - always handy (same with actually paying attention to someone’s name when they say it, but I digress…).
One younger company also made a point that everyone was informal to each other. A bit strange at first to be saying “du” to the CEOs (kind of like: “Hi, Bob!”).
Usually I get away with any unintentional mistakes, since everyone can tell I’m a foreigner due to my accent…
NB
I know that I was just saying that the way you know it in Spanish is the same way you know it in English, it’s context-based. And as for “when do you change,” again it’s context-based.
President Mitterrand supposedly once responded to this invitation with a bleak “Si vous voulez”
There are three levels of formality available to a speaker of Brazilian Portuguese, and of these, two are rarely used by the younger generations.
Day-to-day speech between Brazilians uses você for “you”, and I imagine you can get along your whole life with just that form (I know I do!)
The language enjoys the same tu forms that Spanish has, though I have only heard proper usage as a subject (with different verb form) coming from older people.
Many times you will hear the direct/indirect object form of tu spoken, incorrectly intermixed with sentences containing você: Eu te ligo amanha—você tem meu celular? “I will give you a call tomorrow—do you have my cell phone number?”.
The more formal form is an oddity that uses an unusual third-person form to speak to a person in front of you, like “Would sir like more kidney pie?” or “Is madam ready to go to the play?”
I hear this all of the time in conversations between my wife and her elder relatives, taking the form o senhor or a senhora: A senhora gostou do presente que eu mandei? “Did you (formal female) like the present I sent?”
I liken this third form to the way that kids used to always say Mr./Mrs. to grownups when I was young, but nowadays it is not so unusual hearing teenagers calling adults by their first name.
I certainly hope I am not offending my wife’s family when I stick with the vanilla você, but in twenty years nobody has said a thing about it.
Which meant…?
Yes. At least in Dutch I cannot imagine using the formal on date.
I’d imagine you’d have picked that up by a raised eyebrow or similar facial expression, rather than having a verbal discussion about it. I would just switch back without apologising.
Yes. I used a “Sie” to a German colleague and she immediately told me to call her “du”.
Generally, in The Netherlands the formal form is not used that much, but I personally do like to use it when appropriate. IMO the further south you go, the more it tends to be used, and in Flanders they use it yet more, so there can be a regional aspect as well.
I once received an information leaflet from a hip-ish travel agent’s with which we had booked a trip addressing the participants in the informal “je”. I didn’t like that, but I can see how other people would have appreciated the informal, easy-going atmosphere this usage created, so even for native speakers it is not always clearcut.
“Si vous voulez” means “If you wish.” However, the point is that he is using the polite form “vous” – if he were really responding to the request, he should have said, “Si tu veux”, which has the same meaning, but uses the informal “tu”.

Which meant…?
He’s saying “If you like.” but using the formal second person to show what he thinks of the idea.
This is speaking from Quebec:
As others have said, you know it’s ok to change from vous to tu in the same way you would know it’s ok to go from the person’s name last or title to the person’s first name. When you first do so, there may be some anxiety if you’re risking offending someone who has authority over you.
I guess the main way to know is to ask yourself if it would be appropriate to invite the person for a drink.
Date: You would always use tu. I heard that Jacques Chirac would use vous with his wife, I don’t know if any froggies can confirm this.
Colleague: Depends on the workplace. In a blue collar job, would be likely to use tu except between managers and subordinates who don’t often see each other. In a law firm, articling students would use tu between themselves. I saw a stuffy law firm where articling students and secretaries used vous to talk to lawyers but lawyers used tu to talk to secretaries and articling students.
In the military, soldiers of the same unit and roughly same rank would use tu, especially among the junior enlisted. The higher up you go, the closer the ranks have to be to allow tu.
In my anthropology classes, tu was usually used between teachers and students. In philosophy, it was a mix of both. In law, vous was always used, to the point where a student using tu to ask the teacher a question drew whispers.
Offense: You would switch to using vous. Perhaps apologise. I’ve never seen someone show they were offended.
Right-off-the-bat: All the time. In fact, saying “Call me Bob” would be taken to mean “use tu”. To call someone by his first name and use vous would be incongruous and vice versa.

Generally speaking, in Quebecois French, if you’re introduced to someone by their first name in a social situation, ‘tu’ is ok. If you’re introduced by surname or it’s a business encounter, ‘vous’ is the way to go. If/when these people say “oh, please, call me (Firstname)”, you can generally switch to ‘tu’ with them as well.
I recall my boss of about 20 years ago, a Québecoise lady in her late 50s, coming back from the bank one lunch hour incensed that the teller had dared to tutoyer her without permission!

Date: You would always use tu.
So that Lady Marmalade song from the 70’s was sort of an oxymoron, then?
(then again, if you’re into orgies, maybe not)

So that Lady Marmalade song from the 70’s was sort of an oxymoron, then?
(then again, if you’re into orgies, maybe not)
I think maybe the subtext was that either (a) the request-maker didn’t understand French half so well as he thought he did, or (b) though he was prepared to ask her to engage in sex, he was not intimate enough with her (in the friendship sense) to tutoyer her. In either case, it’s an ironic comment on the character the singer is portraying.

I recall my boss of about 20 years ago, a Québecoise lady in her late 50s, coming back from the bank one lunch hour incensed that the teller had dared to tutoyer her without permission!
It did happen some time ago, and with a person who was already relatively old. I’d say that as a rule people in Quebec tend to be more informal than people in France, though it may be changing. People who don’t know each other will very often automatically use tu here, which I understand is not usually done in France except among young people.
I myself tend to use vous more than other people my age. With my students, I mix both, and one of my former students who later became my girlfriend told me she really didn’t like me calling her vous. (Of course I’d already switched to tu when we became friends.) Just a few hours ago I was with a student, and while I used tu with him, he used vous, possibly because he was there to convince me to increase his grade. I will admit that I’m never quite sure what to use with my students.

I think maybe the subtext was that either (a) the request-maker didn’t understand French half so well as he thought he did, or (b) though he was prepared to ask her to engage in sex, he was not intimate enough with her (in the friendship sense) to tutoyer her. In either case, it’s an ironic comment on the character the singer is portraying.
I can’t think of a way to check this, but I’d think the main reason vous was used in that song is because of the alliteration.
It’s also got the right number of syllables to match the music’s rythm.

I think maybe the subtext was that either (a) the request-maker didn’t understand French half so well as he thought he did, or (b) though he was prepared to ask her to engage in sex, he was not intimate enough with her (in the friendship sense) to tutoyer her. In either case, it’s an ironic comment on the character the singer is portraying.
Err, no. The rest of the lyrics make it pretty explicit that that Lady Marmalade is a prostitute. She’s asking a Joe if he wants to sleep with her, someone she obviously doesn’t know. Hence the “vous”.
Of course, IRL prostitutes tend to use “tu” anyway, or so I heard, so it’s still the wrong turn of phrase

To call someone by his first name and use vous would be incongruous and vice versa.
In France, actually, it does happen in some workplaces. So, a boss could be called by his first name, but using “vous” : “Je vous ramene le rapport, Michel”. Never the other way around though (“tu” + Mr Boss).
By the way, in two different periods of my life, I’ve been called using the third person “il” by coworkers. I interpret it as a “not sure if I should use “vous” or tu” in some segments (blue collars, apparently, but not at all all of them, it’s very unusual) of the population. The first time, the “il” stuck (I used “vous”), the second time the “il” eventually dissapered to be replaced by “tu”, except one worker who opted for “vous” (we had come to dislike each other).
The first time, I was working with older females, so I used “vous” myself". The second time (men my age) was more disconcerting since I wasn’t sure whether to use “tu” or “vous” myself (and switched back and forth).