Which is grammatically correct and why:

Each of you were asked to do this.

OR

Each of you was asked to do this.

This is what Random House Unabridged Dictionary says about your dilemma:

—Usage. The adjective EACH is always followed by a singular noun: each person; each book. When the adjective follows a plural subject, the verb agrees with the subject: They each dress in different styles. The houses each have central heating. When the pronoun EACH comes immediately before the verb, it always takes a singular verb: Each comes (not come) from a different country. When the pronoun is followed by an of phrase containing a plural noun or pronoun, there is a tendency for the verb to be plural: Each of the candidates has (or have) spoken on the issue. Some usage guides maintain that only the singular verb is correct, but plural verbs occur frequently even in edited writing.
It is also sometimes said that the pronoun EACH must always be referred to by a singular pronoun, but again actual usage does not regularly observe this stricture: Each member of our garden club had their own special interests. In the most formal speech and writing, singular verbs and pronouns occur more frequently than plural: Each member … had his own special interests. The use of plural forms, especially plural pronouns, has been increasing in the United States, partially because of the desire to avoid using he or his to refer to a female.

CB