I think you are asking for things that have an influence on Hamlet's behavior and attitude in the play. If so, here are a few things to consider.
One strong influence on Hamlet are his religious beliefs. He vehemently opposes the marriage of his mother and his uncle because he regards it as incestuous, as would have the Catholic church at the time. He also considers suicide, but doesn't do it because it is against God's laws.
The ghost influences Hamlet to take vengeance on Claudius for his murder. He makes sure to tell Hamlet exactly what happened to him and how he feels about the marriage of his wife to his brother so that Hamlet will feel the emotional tie to his father and do what he is told to do. When the ghost returns in Act 3, Hamlet is influenced to stop being so harsh with his mother and focus his attention on the task of vengeance.
Fortinbras influences Hamlet from afar. Hamlet sees Fortinbras going off the Poland to fight over a worthless piece of land and Hamlet is then inspired anew to take his vengeance against Claudius -- to fight for something that is very worthwhile and dear to him.
Claudius influences Hamlet to do he needs to do to save himself. Hamlet reads Claudius's note intended for the English king, and decides re-write the note to condemn Rosencrantz and Guildenstern. This isn't something he would have done in other circumstances, but Claudius kind of forces his hand.