Compelling and relateable is a good starting point, but for someone to be relateable to me is usually quite a bit different for me than someone else. (I found Squall at the beginning of FF8 relateable, but by the end of the game I was ready for him to die in a fire.)

Generally if they are someone I am looking for a connection with I want either:
a) A very self reflective type of character
b) A bad ass character

Or possibly both.