Are there any words that only exist in the Plural Form? One example that I have heard of, but am not sure about, is Hustings.
There are quite a few words that fall into this category. Names of instruments: bellows, binoculars, forceps, gallows, glasses, pliers, scissors, shears, tongs.
Names of articles of dress: braces, briefs, flannels, jeans, knickers, pants, pyjamas, shorts, tights, trousers.
There is also the more difficult category of words ending in -ics which may or may not govern a plural verb. Such words used strictly for the name of a subject are regarded as singular: Economics, Ethics. Compare heroics, hysterics.
Hustings, by the way, was used in the singular, but only in Old and Middle English.