Some attributes I've read people with Asperger's have:
-Tendency to over-analyze problems and social interactions after the fact
-Despite the above, many have a tendency to be impulsive--which bleeds into saying things before thinking about them
-Awkward in relating to NTs
-Tendency to say exactly what's on their mind, despite of its appropriateness
-Comorbid conditions such as depression, anxiety
-Tendency towards negative thinking, probably due to depression/anxiety
-Obsessing, and in an individual with comorbid depression, obsessing about death
I feel like Hamlet displays all of the above qualities, and more (its been a while since I've read it). Through the play he is busy over-analyzing his problems/social interactions (so much so that that is his tragic flaw). The few times he manages to bring himself to action he does so impulsively and suffers the consequences. His interactions with his Mother, Ophelia, and others are humorously awkward throughout the play. He's constantly speaking his mind--which is hilarious, especially with the puns--though no one pays him any mind it seems. He's obviously going through depression and/or anxiety issues throughout the play (though its likely just due to his father's untimely death, it may also be due to a life-time of awkward interactions with others, and the inability to understand and be understood by NTs). He spends most of the play moping and letting his thoughts travel toward negativity. And of course, the entire play is about him obsessing about death. Mind you, other non-Aspies could have all of these traits, but its still an interesting connection.