I'll start this off by saying that I have known some very capable musicians over the years, and some had an almost encyclopedic knowledge of theory, and some wouldn't admit to knowing any at all.  So I don't think that it is a reflection on how one actually plays so much as "Different folks are different" in how we conceptualize and understand things.  Since I've known fine players on both ends of the spectrum, it seems logical to me to think of it more as a difference in how people conceptualize and understand than considering it an actual requirement for proficiency.

The question is "How important is theory to you personally, as a musician/player?"

Personally, I studied it a bit in books and magazine articles and took a couple semesters of theory class back in college.  I feel I do probably apply it, since I'm usually aware on some level of things like when moving from one note to another, I may note that I'm moving up a 5th or down a minor 3rd, and I sometimes will make a mental note of if I am shifting mode.  But mostly, I conceptualize music as sounds when I am playing.  I'm not thinking "Ah, and here I'm moving to the 4th degree mode of the scale" or even "Oh, hey, that's an A note" when I'm playing.  The exception to that would be if I'm working out some accompaniment to a piece, where I will make mental note of at least the notes of a melody that I want to build the accompaniment around.  

But most of the time, I don't make an active deliberate use of what I know of theory while actually playing.  I focus more on the sounds and how the melody feels as it moves from one note to another.  That may be at least partially due to having learned by ear before studying any theory, so theory became sort of a framework for understanding what I do more than a set of rules to do things by.

I'm wondering how many folks here have made some study of music theory, and whether you feel you apply it when playing and if so, how you apply it.