I think he will be remembered as a man who dealt with an increasingly cannibalistic GOP, didn't really handle it well, and ultimately it consumed him. From what I've read, his relationship with the President is pretty poor, even as Mitch McConnell and Joe Biden managed to get things done together. That being said, I think its more the first thing, the cannibalistic House GOP, then anything wrong Boehner was doing (Though I'm not sure he's that competent, he was kind of a "let's calm down guys" pick to replace Denny Hastert).
Ultimately I don't think he will have much of a legacy. He wasn't so controversial like Speaker Gingrich, and doesn't really compare to most speakers in terms of accomplishments.
