What can we learn from Hamlet's soliloquies?

For starters, we learn what Hamlet thinks about himself,
life, death, Denmark, his mother, Claudius.  From his first soliloquy, "O that this too
too sullied flesh should melt,"  we learn that he is close to suicide over his father's
death and his mother's too soon marriage to Claudius.  We know that he is learned,
scholarly, moral, and deeply disillusioned by those around him.  But we also learn that
he is not quick to action.  He knows he must hold his tongue.  Later, in Act 2, Hamlet
reveals in his "O, what a rogue and peasant slave am I" soliloquy his extreme
frustration over his inability to avenge his father's death.  He is angry that Claudius
lives and that he has been able to do nothing but put on an antic disposition.  But in
this soliloquy, filled with self-loathing and bitterness, we see a very smart mind at
work.  He comes up with a clever plan to ascertain Claudius' guilt.  In his "To be, or
not to be" speech, we see further a more mature mind as Hamlet philosophically and
rationally considers why people endure suffering in this life when they could take
action to end this suffering.  This speech marks a certain development in Hamlet's
character in that it is a general musing rather than an individual expression of
emotion.  In Act 4, Hamlet's soliloquy "How all occasions do inform against me," we see
Hamlet dissect the connection between thought, action, and cowardice as he evaluates the
honor and merit of Fortinbras's actions.

These are some of
the major soliloquies and some brief ideas of what is learned through them.  Through
them we understand Hamlet's developing maturity throughout the play, his impressive
thought processes, and his motivation for acting or refraining from acting.  Much more
could be written on these.