I rooted for Karl!

Revenge is always a powerful and sympathetic force that drives and fuels action hero characters. Other have pointed out that what makes Die Hard unusual, from a narrative structure perspective, is that it's actually Hans and his men who are the protagonists and John McClane who is the antagonist.
Karl, like a hero in any Western, is a man on a mission when someone comes along and thwarts his plans and kills someone he loves. He subsequently loses interest in what has hitherto been his objective, which entails the pursuit of material wealth, and redirects all his energy toward pursuing a far more noble goal--honoring a fallen comrade, and loved one, no less. Once he loses his brother Tony at McClane's hands early in the film he subsequently spends the last few hours of his own life dedicated and devoted to avenging his sibling because he loves him so much.
The rage and grief in Alexander Godunov's face that he shows for the rest of the movie has always deeply touched me, and truly rams home the point that Karl is a man who puts family above all else and will do anything for those he loves. The way he flies into a rage and flips the table over in the office crying out for McClane's blood is haunting and moving, as is the conviction and fervor with which he tells his subordinates "No one kills him but me!"
He reminds Hans that he doesn't want McClane neutralized, but dead.
When he at last has his chance to even the score for Tony he takes his time kicking McClane to death because he wants him to suffer. Alas, this permits McClane to acquire the upper hand and kill *him* and Karl's determination to avenge his brother enables him to not only come back to life but survive an explosion and make one final, last ditch effort to send his brother's killer to his own Maker, in full view of hundreds of witnesses. Karl doesn't care if he goes down in the process. All that matters is punishing the man who took his one and only beloved sibling from him.
We should all drink to Karl Vreski. The terrorist/thief who ultimately put FAMILY above everything else.