What do the characters Macbeth, Hamlet and Othello have in common? I know they're all tragic heroes and I know why, but I can't seem to work out...

There are a lot of things each character has in common. 
First and foremost, all there are tragic heros who have lost control of themselves.  As
for the how and why of losing control, that varies.  It can be argued that "love" plays
a major role.  All three men allow (willingly or unwillingly) the women in their lives
to manipulate and twist their feelings.  Macbeth allows Lady Macbeth to fuel his desire
for power, Othello allows his jealousy of Cassio and Desdemona's affair (or thought of
affair) turn his well-known strenght and honor to nothing.  Hamlet's love of Ophelia can
be said to springboard his "maddness."

Some other things in
common:

-revenge

-power

-supernatural
(Othello's vodoo religion would be the stretch here)