In Hamlet, what are some distinctive qualities of Hamlet's character other than his being overly given to thoughtfulness?I'm writing on how...

Maybe these will help:

1.  He is intelligent and highly educated.  He can use allusions to Greek and Roman mythology as well as to the bible.  These allusions are somewhat obscure:  Niobe, Hyperion, Mars, Jepthah.  He can recite long speeches from plays he has heard.

2.  He is well versed in drama.  He even gives the actors instructions on how to act.

3.  He is idealistic.  Because he is idealistic, he is very disappointed when others do not live up to his expectations.  We see this especially in his relationship with his mother.

4.  He is emotional.  He feels deeply.  He continues to mourn his father's death long after others have moved on.

5.  He is not only tough on others, but he is tough on himself.  In the last scene of Act 2, he is furious with himself that he has not acted to avenge his father's death.  In Act 4, he feels that Fortinbras is accomplishing more than he is.  But he is also tough on others:  he lectures his mother in Act 3, for instance.

6.  He is loyal to those who deserve it, and he is a good judge of characters.  Look at his relationship with Horatio, for example.