Perhaps his most famous soliloquy, Hamlet debates even existence in Act III, Scene 1.  For the first time, Hamlet contemplates suicide and shows signs of mental deterioration; clearly, he is in a state of deep melancholy.  Also, he wrestles with the problem of avenging his father's death, for Hamlet is not totally convinced that King Hamlet's ghost is real; added to this, he debates whether he wants to commit regicide, a very serious offense.  Nevertheless, after this moment, he does become consumed with the idea of revenge.

Along with the themes of mental deterioration and revenge, the theme of death is introduced with this soliloquy.  All these ideas are too much for Hamlet:

And thus the native hue of resolution/Is sicklied o'er with the pale cast of thought,/And enterprises of great pitch and moment/With this regard their currents turn awry/And lose the name of action. (III,i, 84-88)

He is incapcitated by his depression.  His fixation on avenging his father's death, combined with the confusion this brings to his sense of morality, causes Hamlet to become helpless.

The tone of this soliloquy reflects the tone of the play: chaotic and pessimistic.  Hamlet waivers with indecision throughout the soliloquy as he does throughout the play.  In subsequent soliloquies he weighs the senselessness of other actions in life, such as that of Fortinbras who willingly goes to a worthless battle against the more reasonable revenge against Claudius, yet he remains indecisive.  When he does act, his actions seem hasty and impulsively with tragic results such as his stabbing of Polonius behind the curtain.