I understand I'm in the extreme minority and it's kind of become a musical credibility killer to admit this, but I do like Fall Out Boy. I have everything they've ever released in my collection, and they're my most listened-to artist according to my Last FM page too. From Under the Cork Tree (2005) was one of my favourite albums of the last decade.
As a long-time fan of the band, I find their singles are easily the worst songs on their albums. So for those that don't like them, I encourage you to look beyond their singles, because that's where there best songs actually lie.