When using the Harvard system of citation (or any other system for
that matter), is it correct to cite the date of the book's orginal
publication or the date of the edition which you used? E.g. I am
writing an essay which uses the novek Bread Givers by Anzia Yezierska.
Do I cite it as (Yezierska 1925) or (Yezierska 2003)? And similarly,
in the bibliography, which date do I include; or if both, in what
format? Thank you!

According to 
http://en.wikipedia.org/wiki/Harvard_referencing
you would cite your reference as

(Yezierska 1925) 
if you had used the 1925 edition, and as

(Yezierska [1925] 2003) 
if you had used the 2003 edition.

Also, you might add the page number in the edition you used, like this:
(Yezierska [1925] 2003, p. 123) 

The bibliography would appear like this:
Yezierska, Firstname [1925] 2004 Title of book Edited by Editor.
Location: Publisher name.

This link provides extensive details (although I notice it has
inconsistent examples):
http://library.curtin.edu.au/referencing/harvard.pdf

I hope that this is useful, until a researcher gives a more definitive answer.

Most of the "rules" for citations, such as those referred to by
forumbob above, are designed for references to non-fiction books,
journals etc, where you're quoting or referring to the research
findings or opinions of other authorities. But this doesn't seem
appropriate if you're quoting from a fictional work, as you're doing.
Assuming that prior to the first quotation, the book, author and date
of first publication have been stated in your text, then the page
number would be sufficient. For subsequent quotations, the title and
page number in brackets might be needed. Then in the bibliography, you
would, as forumbob says, give details of the edition you have actually
used. (Writers often use an abbreviated title in bracketed citations -
eg BG for Bread Givers; with the abbreviation explained in the
bibliography.)