Claudius

                 "But to persevere in obstinate condolement is a course of impious stubbornness. 'Tis unmanly grief;" (I.1.93)
                  This statement is one of the most ignorant one I have ever heard. It establishes Claudius as an unsympathetic, unreliable, untrustworthy uncle. The poor boy just lost his only father! And yet Claudius essentially tells Hamlet to "forget about it". Hamlet has every right to dislike his uncle now.

                   "There's something in his soul o'er which his melancholy sits on brood; And I do doubt the hatch and the disclose will be some danger" (III.1.166)          
                     Now he is suspicious that Hamlet knows. He cannot take the pressure of his own nephew knowing that he killed his uncle, and so he does not mention what he thinks Hamlet is brooding over. Also, Claudius plays on the "squash the serpent while it is still in the egg" analogy. He wants to get rid of Hamlet before he explodes and has bad consequence. He is being precautionary.

               "My words fly up, my thoughts remain below. Words without thoughts never to heaven go."(III.3.96)
                The prayer that he tries to conjure when he is on his knees is useless because he does not feel repented. He says the words that what he has done is wrong, and attempts to relieve himself of this burden, but alas he cannot. It is a shame too because Hamlet would have killed him right there if he did not look like he was being earnest in praying. Claudius is not sincere of repenting of his faults and honestly this prayer is probably just a way to make him feel better.

                 "Do not fear our person. There's such divinity doth hedge a king that treason can but peep to what it would, acts little of his will" (IV.5.122)
                   Very ironic, considering that he has just killed a king himself. Claudius is proving to be shallow, very shallow indeed. He contradicts himself, he is ignorant, he murders to marry, and he tries to forget his faults. And he has such confidence in himself that it is ridiculous.

                 "The Queen his mother Lives almost by his looks; and for myself,- My virtue or my plague, be it either which,-She's so conjunctive to my life and soul That, as the star moves not but in his sphere,I could not but by her"(IV.7.12)
                   Well, I believe I have found the one good quality of Claudius. He really loves his wife, and the reason that he keeps Hamlet is because he knows his beloved wife loves him so. He is loyal to her, and that is something good. He recognizes that this hesitation to completely get rid of Hamlet is either a bane or a benefit.