The link at the top (https://scontent-a-dfw.xx.fbcdn.net/hphotos-prn1/1520827_339527339521398_123074705_n.jpg) is dead
I'd want to edit a good chunk of these, particularly the examples in Homestuck (since I'm familiar with that fandom), but I'm kind of overwhelmed. It seems like a lot of people mistake this trope for Love to Hate, Evil Is Sexy, Evil Is Cool, or (and especially) Sympathy for the Devil. Liking a villain character is not this trope. Thinking/depicting a villain as sexy is not this trope. Feeling bad for a villain is not this trope. What is, you may ask? If the fans deny outright that the villain is at fault for what he did, and pretend he is little more than a straight-up misunderstood Woobie, Destroyer of Worlds (or hell, just The Woobie), and cast him as a sweet, if aloof, little darling that is completely unrecognizable by his characterization in canon, then it becomes this trope.
It bugs me because I see a lot of instances of tropers getting worked up when a fan so much as sees a villain as a Jerkass Woobie (note that in this case, that still makes the character a jerkass - in other words, even those who feel pity would gladly deliver a backhand for being a douchebag), regarding it as this trope.
Would sacrificing their own life to save someone else's life count as a "redeeming quality?" I feel like it's missing from the redeeming qualities of one of the characters.