Yes, definitely a girl & a boy can be best friend.
To become a best friend one does need a sense of great understanding. Gender does not become a barrier between the friendship between the two sexes.
Though in India people's mindset are orthodox type which sees the friendship of a boy and a girl in a different sense but in reality,this is the thing which should be changed.
A friendship of a boy and a girl can be as normal and as pure as the friendship between Lord Krishna and his best friend Draupadi. The understanding,the protectiveness,the caring & the loving nature of both of them can make them the greatest of friends irrespective of their gender.