"I wish it were Friday" uses the past tense of the subjunctive mood, which is the tense used to express wishes (but it is also used for imaginary or hypothetical situations).
"I wish it was Friday" is nowadays used too, probably because "I wish" makes already evident that the sentence is about a wish.
The NOAD reports this notes about the subjunctive mood:
"If I were you"; "the report recommends that he face the tribunal"; "it is important that they be aware of the provisions of the act". These examples all contain a verb in the subjunctive mood. The subjunctive is used to express situations that are hypothetical or not yet realized and is typically used for what is imagined, hoped for, demanded, or expected. In English, the subjunctive mood is fairly uncommon (especially in comparison with other languages, such as Spanish), mainly because most of the functions of the subjunctive are covered by modal verbs such as might, could, and should. In fact, in English, the subjunctive is often indistinguishable from the ordinary indicative mood since its form in most contexts is identical. It is distinctive only in the third person singular, where the normal indicative -s ending is absent (he face rather than he faces in the example above), and in the verb "to be" (I were rather than I was, and they be rather than they are in the examples above). In modern English, the subjunctive mood still exists but is regarded in many contexts as optional. Use of the subjunctive tends to convey a more formal tone, but there are few people who would regard its absence as actually wrong. Today, it survives mostly in fixed expressions, as in "be that as it may"; "far be it from me"; "as it were"; "lest we forget"; "God help you"; "perish the thought"; and "come what may".