By the LoTR poll, I’m an outlier - my favorite three are Boromir, Faramir and Theoden! And for similar reasons - they’re important, and IMHO nuanced characters that feel far more ‘real’ to me that the rest.
Boromir, who is desperate, trying to keep his people safe and alive, and tempted (like everyone) with the great good he could do with such power. Who fails in a moment of weakness, but still manages to live up to his ideals. And his portrayal in the Jackson movies was spot on for me!
Faramir, although not as developed as I like, because he serves as a mirror - given an advantage of perhaps less crushing expectation (although with equally crushing less respect and love), and certainly less exposure to the the ring, manages to be one of the very very few beings who turn away from the ring, albeit with the additional warning his prophetic dream gave him.
He stands and does his very best, even if he’s not at the levels of the heroes around him, and for that he’s one of my favorites.
Lastly, Theoden is most interesting for his flaws. A great ruler of men, brought down by conspiracy, poor advice, and hubris. But one who does not abandon his responsibilities despite legitimate issues, even if he does put his own people first. And of course, the Jackson portrayal does an incredible job with this character as well.
So yes, my favorites all share the theme of their flaws, their lack of plot armor, and a shared sense of tragedy. 
Now if you had asked me this question when I was in my teens, the answer would have been very very different!