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I have trouble with the following question:
Father says that either you or I (is, am, are) to blame for the broken window.
I think 'is' is the correct answer but my teacher says 'am' is the correct answer.
Please help.

I think your teacher is right: (is , am, are) should coincide with the last subject( in your sentence it's "I') . So - I am to blame....

"Am" is correct, but "are" is also acceptable. Definitely not "is."

Note that there are ways to avoid the problem altogether:

"Father says that either you are to blame for the broken window or I am."
"Father says that one of us is to blame for the broken window."
"Father says that the blame for the broken window rests on either you or me."

Chrisooi wrote:I have trouble with the following question:
Father says that either you or I (is, am, are) to blame for the broken window.
I think 'is' is the correct answer but my teacher says 'am' is the correct answer.
Please help.

"Is" would not be correct. "Is" is used for third-person singular pronouns (he, she, it).
Use "am" since it follows "I" ("I am to blame").
If you rewrite it "Father says that you", then you "are".

Father says that you or I am to blame.
Father says that I or you are to blame.

As JCloninger implies, the general rule is to conjugate the verb for the subject closest to the verb.

Father says that you or I are to blame.
This sounds find to me.

Father says that you or I is to blame.
This sounds ok, but not as good as the first one.

*Father says that you or I am to blame.
This sounds very weird to me.

I don't think the principle of proximity applies here. Would anyone say "The horses and the dog is very well behaved today"?

The principle of proximity applies to situations where there is some distance between the noun phrase head of the subject and the verb usually because there is a length postmodifier, as in "The filing of the false, fraudulent charges are a complete contraction" (Joseph McCarthy) where the subject NP is singular but the modifier that is closest to the verb is plural.

But that's not what's happening in "Father says that you or I am to blame." Here we have a compound subject: two pronouns conjoined by "and". My intuition is that the plural verb is better here. According to Merriam-Webster's Dictionary of English Usage, the plural verb is usually used with compound subjects (singular nouns compounded by "and").

anderson wrote:Here we have a compound subject: two pronouns conjoined by "and"

There is no "and" in the original sentence.

right, they're conjoined by "or" not "and". The principle is the same.

anderson wrote:right, they're conjoined by "or" not "and". The principle is the same.

No, I'm wrong. For pronouns joined by "or", MWDEU says

Compound singular nouns with or or nor are supposed to take a singular verb and in current use usually do. The plural verb is most likely to appear where the notion of plurality is suggested by negative construction or when the writer is thinking of "this or that or both".