What does Hamlet mean when he says "Give me that man that is not passion's slave" in Shakespeare's Hamlet?
One significant theme of this play is the tension between passion and intellect. People with a lot of passion (not necessarily romantic passion) act rashly; they do what they have to do without a lot of concern for the possible negative consequences. People who are the opposite of that, the intellectuals, think more than they act; they weigh the potential consequences of their actions, and in many cases this thinking holds them back from action. Finding the right balance between thinking and action is what Hamlet struggles with through the entire play. Hamlet's quote from above is actually part of a longer sentence that really needs to be considered in its entirety to be understood. Hamlet's complete thought is this:
Blest are those whose blood [passion] and judgement [intellect] are so well commingled / That they are not a pipe for Fortune's finger to sound what stop she please. Give me that man that is not passion's slave, and I will wear him / In my heart's core.
Hamlet recognizes that the best people are those that find a perfect balance between thinking and action so that they do what they need to do, but don't act rashly and then cause unnecessary trouble. He claims that people who act with too much passion are the plaything of Fortune. In other words, they give too much of themselves over to fate and have a "what will be will be attitude" which can be dangerous if taken to an extreme. That is why he doesn't like or respect people who are slaves to their passions. People like that can create a lot of havoc in the world. From his own experience he is clearly referencing King Claudius who seems to be a slave to his passions and personal desires.
The resolution of the play comes, in part, from Hamlet being able to give himself over more to his passion and less to his intellect. Once he stops over-thinking, he can actually act to take his revenge against Claudius.