Well, the title explains it all! Discuss!
To start, some of my favorite FoB songs are...
Sugar, We're Going Down:
Thnks Fr Th Mmrs:
Grand Theft Autumn/Where Is Your Boy:
I Don't Care:
This Ain't a Scene, It's an Arms Race:
and The Take Over, The Break's Over:
You forgot Dance Dance
I myself really like Centuries, Alone Together and My Songs Know What You Did In The Dark (Light 'Em UP) #LongestSongTitleEver
I like none of those except for Alone Together. 
Yeah, their newer albums seem to be more then a bit polarizing.
all my yes
Say who's heard of their song Roxanne?
Rat a tat is one of my fave songs but I've had Thnks Fr Th Mmrs in my head for a while now
Rat-a tat tat, rat-a tat tat tat
AY!
Im playing Thnks fr Th mmrs right now and head banging to it
here are two more good songs. look out for the falling hand
You should see their old songs...
I'm mostly a fan of 2004-2009 Fall Out Boy. My favorite album overall is Folie á Deux, though I like each of their first four. Some (read: an excessive number of) favorite songs that maybe aren't as well-known:
They have a solid 4 songs I called myself a fan of.
Also, The Young Blood Chronicles was a pretentious and pretty meh album..film...video...thing.
The Phoenix was a good song from that though.
And I guess the one with Elton John was okay.
Otherwise, I liked Dance Dance, Thnks fr th mmrs, and Centuries. The first two I cannot justify, but I have a very spefic reason for it.
Agreed. I also kinda like immortals..I have not heard much else from them...
I've heard of the first two but I never cared for each of them
I get the idea we have completely different tastes in music. 
I really liked the YBC...
I have infinity on high I though it was OK but I haven't seen enough of the rest of their music to say much.
I haven't heard much of theirs but Centuries is pretty great.
I've only heard
and it didn't do much for me. I haven't listened to much else from them.