What does Claudius say he gained by killing King Hamlet?
In act 3, scene 3, Polonius leaves Claudius by himself to pray at his altar, where Claudius admits his motivation for killing his King Hamlet. Interestingly, Claudius mentions that he will not ask God for forgiveness because he is unwilling to surrender his ill-gotten rewards. Claudius says that he is still reaping the benefits of his crime by saying,
"That cannot be, since I am still possessed Of those effects for which I did the murder: My crown, mine own ambition, and my queen" (Shakespeare, 3.3.54-56).
Claudius has not only gained the authority and power of becoming the King of Denmark but has also satisfied his ambition and married Gertrude. In addition to gaining the throne, marrying the queen, and satisfying his ambition, Claudius also inherits guilt and a tortured spirit, which inevitably come along with committing such a heinous act. Claudius is clearly tortured and filled with guilt, and knows that he will be judged in the afterlife for murdering his brother. However, Claudius is unwilling to ask for forgiveness and instead asks for angels to bow his "stubborn knees" and soften his heart.
In his admission speech (Act 3, Scene 3), Claudius bares all. He, in obvious turmoil, states how his "...stronger guilt defeats [his] strong intent..." (line 40) He is even brought to the point where he states his motives: the crown, his ambition, and the queen (line 55). Even though the murder he committed was awarded with power, pride, and a beautiful queen, the guilt his has acquired is much more prevelant and severe. At the end of his speech, he makes one last attempt for redemption; he cries to the angels, "Help, angels! Make assay./Bow, stubborn knees; and heart with strings of steel,/Be soft as sinews of the new-born babe./All may be well." (lines 69-72)
Quotes taken from The Norton Shakespeare: Based on the Oxford Edition.
You need to have a look at Claudius' prayer speech in Act 3, Scene 3. He speaks the following lines, wondering whether he can be forgiven for his crime:
I am still possess'd
Of those effects for which I did the murder—
My crown, mine own ambition, and my queen.
Claudius killed Hamlet for his crown (that is, to become King of Denmark), to serve his own ambitious nature, and in order to marry Gertrude, the Queen of Denmark.