Really it isn't just House of Cards lately that I've been seeing so much Shakespeare in, Breaking Bad and True Detective also have turns and handle archetypes in a way that strongly reminds me of what I've been teaching for the past couple of weeks.
We just finished a Unit on Macbeth with the Seniors and this is the second year that I have taught Macbeth. I have to say that watching the whole series of Breaking Bad over Christmas break was a great way to get ready to teach this play. There are so many correlations between Walt's downfall and Macbeth's (though Skyler is reluctant while Lady Macbeth wears the pants in the evil).
Francis' relationship with his wife in House of Cards is decidedly better(?) than that of Iago and Emilia in Othello (though if they are at odds with one another in Season three and he decides that she is a liability then things will align a bit better). Claire is complicit in a much more Lady Macbeth manner than Emilia is to Iago's evil plans in Othello. The way Francis interacts with Chloe (spoilers) is also very much the relationship between Iago and Roderigo in Othello (the power in the relationship is extremely one sided and when Chloe/Roderigo becomes a threat they are easily dealt with).
I think it is kind of poetic (ironic?) that television has become the most likely medium for long form studies of archetypes the way Shakespeare did. Hank plays a wonderful Macduff for a while and Jesse Pinkman makes a great Roderigo again (especially when Walt keeps reeling him back in with flattery).
That television is beginning to take Shakespearean ques also should open up a wealth of opportunities for Undergraduate Courses. Imagine a Shakespeare and Television course studying Vince Gilligan.
On a separate note, I need to read Richard III because Francis is supposedly also based off of that play.