I'm tempted to dub Francis Underwood the greatest antihero of all time, but I'll play it safe and say the greatest antihero in recent memory. What is so striking to me about him is that he is really a terrible person--over the course of two seasons of House of Cards, we see ever increasing levels of self-centered ruthlessness--and yet the viewer is on his side. I am, anyway; maybe not everyone sees him that way. I would particularly contrast him with Walter White, who in my view evolved from a hero to a villain over the course of Breaking Bad. His character is interesting in a very different way: we see a good man become bad, squandering virtually all of the viewer's sympathy by the end of the series (again, to me, but perhaps not universally). I can't put my finger on the difference in the characters' ability to evoke sympathy, since their misdeeds are fairly comparable. Is it Frank's statesmanlike bearing that does it? Is it his South Carolina accent?
Surely there has been much written about the antihero, from classical literature to modern popular culture, and I'm not sure how fairly Wikipedia represents all that; but I didn't much like the definition I saw there, and I had lots of disagreements with the list of antiheroes. Some of them (Satan) are really just villains; lots are heroes, with some complication of character or history not severe enough to warrant the "anti" (Shrek, Angel from BtVS, Oh Dae-su from Oldboy, Veronica Mars); and some are no kind of hero at all, just characters with some mix of sympathetic and objectionable characteristics (George Costanza, David Brent from The Office). There were lots of good ones there, though, like Jack Reacher, Tony Soprano, and Greg House: these are at least the same species as Frank Underwood, though not writ so large.