A great example I can think of:
"Please, leave! I would be alone!"
With would meaning something like, "I want to be alone." Is this correct, or not?
EDIT: To further clarify, I am not aiming for would like to. My original question/sentence is not a typo.
"Would" conveys a subjunctive, or conditional, meaning. "I would be alone" implies an unspoken qualification such as "if that was possible" or "if I had my way."
"I would be alone" sounds archaic. It recalls Shakespeare's work for many students, and it is sometimes used to suggest an Elizabethan style of diction. In fantasy fiction it is sometimes used to imply the speaker comes from a chivalric or royal court culture, typically English, sometimes French, and, strangely enough, sometimes in shows with supernatural themes (witches, werewolves, demons). As a result, it is a trite construction in popular entertainment, and is a common target for mock usage as well.
Modern use isn't that different in meaning, but in application. "I would like a beer," for example, is common. Add in the implied "if you have one" or "with your permission," and it can sound timid or deferential, but most people do not take note of that and consider it synonymous with "I will have a beer."
You'll hear a lot of this form in political rhetoric, as it implies an important prerequisite to the intention. "If elected, I would institute a flat tax." You'll also hear it, perhaps not coincidently, as a way to avoid lying without actually countering an allegation or circumstantial evidence: "But I would never steal from my boss because stealing is wrong, and I would never do a wrong thing."
It's also used to suggest an alternate outcome if the conditions of the moment were somehow different. "I would cap my reputation every day if everyone would just wait for my answers."
Yes, it is correct; but it is very old fashioned, and you will rarely hear this spoken in modern English.
In older English, the verb will used to have a stronger sense of desire, want than it has now. I would is the conditional of will; in this sense, it indicates a weaker degree of desire. As you have mentioned, this old usage of would to mean would like is now archaic.
It is normal and common to use would to refer to a present-tense wish.
However, it is very unusual to use would be in the way your example does. A more natural way of stating your sentence would be:
I would like to be alone.
Edit: Actually, based on your tag it now occurs to me that your use of the archaic would be was deliberate. In which case, leave it as is.
"I would be alone" is just a slight wording on "I am to be alone", which most have already mentioned is an archaic way of expressing your wishes by describing how you want things to be rather than express what you desire.
I can't help but associate such archaic expressions with "snobbishness" such as how a queen might dismiss her servant. Whether that has any truth or not, it's used commonly in films to demonstrate the snobbishness of a character. In all truth, it probably derived from the ruling class's tendency to speak a more archaic form of english in order to preserve it and consequently such usage is strongly associated with the ruling class or high class in general.
