What types of roles or purposes do women have in the play Hamlet?

I'm afraid, by our standards today, Shakespeare's
Hamlet is quite a sexist play. Viewed from a feminist
perspective, one might say that the play is the result of a patriarchal or
male-dominated society.

The women in the play are victims
at best (Ophelia) and dupes at worst (Gertrude). 

Gertrude
is full of lust, lacks loyalty, is fooled by Claudius, and is killed by mistake from
Claudius's treachery.

Ophelia is dominated by her male
family members, made by them to spy on Hamlet, goes along with it, is abused
and ridiculed by Hamlet, loses her mind and commits
suicide. 

The action of the drama is furthered, for the
most part, by male characters.  Strictly speaking, the conflict is between two male
powerhouses:  Hamlet and Claudius.  Women are
peripheral.

In all likelihood, this was not an issue in
Hamlet's day.  From our contemporary perspective, though, the play is really quite
sexist.  Particularly in the "enlightened" Hamlet's view, the women are nothing more
than whores.