Learn English – quite pretty, rather pretty, very pretty in British English and American English

EL&U member Farid points the way in his comment earlier. The Longman Online Dictionary (http://www.ldoceonline.com/dictionary/quite) differentiates between American and British English usages. Starting with American English usage:

quite
1 (Especially American English) Very, but not extremely:
'The food in the cafeteria is usually quite good'; 'His hair is quite thin on top now'; 'Amy's at college, and she's doing quite well'; 'He's quite a good soccer player.'

Longman also lists some usages without attributing them to either side of the Atlantic:

3 Quite a lot/bit/few - a fairly large number or amount:
'He's got quite a lot of friends; 'Quite a few towns are now banning cars from their shopping centres.'

5 Not quite - not completely:
'They weren't quite ready so we waited in the car; 'I'm not quite sure where she lives.; Dinner's almost ready, but not quite.'

6 Not quite why/what/where etc - not exactly why, what, where etc:
'The play wasn't quite what we expected.'

Longman suggests that the following are more representative of British usage:

2 (Especially British English) Fairly, or to a small extent, but not very:
'The film was quite good, but the book was much better'; 'I got a letter from Sylvia quite recently'; 'I quite like Chinese food.'

4 (British English) Completely:
'I'm sorry. That's quite impossible'; 'What she's suggesting is quite ridiculous!'; 'I think you've had quite enough to drink already!'; 'That's quite a different matter.'

7 (British English) Quite a something/quite some something. - Used before a noun to emphasize that something is very good, large, interesting etc:
'That was quite a party you had.'; 'The engines make quite a noise.'; 'It's quite some distance away.'

8 (Especially British English) Quite a/some time. - A fairly long time:
'We've been waiting for quite some time now.'

9 (British English) Quite right. - Used to show that you agree strongly with someone:
'I refuse to do any more work.' 'Quite right. They can't expect you to work for nothing.'

10 (British English) That's quite all right. - Used to reply to someone that you are not angry about something they have done:
'I'm sorry we're so late.' 'That's quite all right.'

11 (British English formal) Quite/quite so. - Used to show that you agree with what someone is saying [= exactly]:
'They really should have thought of this before.' 'Yes, quite.'

12 (especially British English) Quite something - Used to say that someone or something is very impressive:
'It's quite something to walk out on stage in front of 20,000 people.'

Longman's Dictionary goes on to observe in relation to American and British English usages:

In British English,using quite suggests you are not very enthusiastic about something. In American English, quite is a stronger way of qualifying an adjective. In both British and American English, the way you say the word is important. In British English, if you say It was quite good and you put the emphasis on the quite, you mean it was good, but not very good. If you put the emphasis on good, you mean it was very good. In British English, when it is used with adjectives like impossible or unacceptable, it means completely, and you put the emphasis on it. In American English, the emphasis is always on the adjective that goes with quite.

Please note that I have made some formatting changes to the Longman text in order to address the question here more clearly. The text in the original format can be accessed at the link above.

It is interesting to consider how 'quite' came to take up this role in signalling emphasis, affirmation, calculation and approximation in language. My understanding is that 'quite' is related to 'quit', but not 'quit' in the commonly understood sense of 'resign', but in it's original (and now obscure) sense of 'calculate, balance, or close an account'.

The OED clearly attributes 'quite' to 'quit' but has nothing to say about the development of the word.

quite ▪ I.quite, adv.
(kwaɪt) Forms: 4–6 quit, quyte, 5 Sc. quhyt, 5–6 quyt, 6 quyght, 6–7 quight, 4– quite.
[f. quite quit a.]
▪ III.quite obs. form of quit a. and v.; white.

When we get to 'quit' in the OED we have to wade through the alternate sense of 'leaving' or 'resigning'. I suggest in my response to EL&U question, How did 'to quit' evolve to mean 'to behave or conduct in a specified way'? that this is essentially the secondary sense, and that the primary sense relates to balancing and closing accounts. Again the OED, in respect of 'quit':

II. 10. To repay, reward, requite (a person with some return for something done). Obs. exc. north. dial. (in phr. God etc. quite, white, twite).
13.. E.E. Allit. P. A. 595 Þou quyteȝ vchon as hys desserte. c 1384 Chaucer H. Fame iii. 524 We han well deserued hyt, Therfore is ryght that we ben quyt. c 1440 Generydes 6975 Thus quyte he them that were to hym so kynd. c 1530 Ld. Berners Arth. Lyt. Bryt. (1814) 178 Syth he had done me one displeasure, I shall quite him agayne with two. 1576 J. Woolton Chr. Manual C i, Let vs not with like thanks quite almightye God for his greate benefyts bestowed vppon vs. 1599 Massinger, etc. Old Law ii. ii, When I visit, I come comfortably, And look to be so quited. 1664 Butler Hud. ii. i. 448, I understand..how to quit you your own way.

So, whenever we say 'quite' we are essentially saying something like: 'by accounts', or 'by my calculation', or 'as the accounts say', or 'considering the balance', or 'as the sums tell us'. Essentially the speaker is referencing an unsubstantiated external authority or body of knowledge or process of developing knowledge to give weight or qualification to an opinion or view that they hold personally.

It is no surprise that it is such a commonly (and carelessly) used word, given that as humans we are very fond of putting our opinions forward, and in the absence of certain knowledge, suggesting with the word 'quite' that the opinion (for better or worse) is not ours alone but references some 'higher' or 'wider' source. One might imagine in future centuries the word 'quite' might have been replaced in this usage by 'wiki'.