I put Three Cheers on earlier for the first time in about 2 years. As far as fast paced melodic post-hardcore goes, its pretty much unrivalled in my opinion, the only album that comes close in that genre is Relationship Of Command. It picks up a pace right from the off and never really lets up (even the slower tracks bear a sense of urgency), with every song packed to the brim full of hooks, and Gerard Way's desperate wail conveying seething anger and utter hopelessness at the same time. I challenge you to find a better post-hardcore album, and even then I'll likely disagree with you.
Anyway, this lead me to revisit their other stuff, and while it doesn't quite pack the same punch as that album, its remarkably consistent. Their debut shows off already strong songwriting while still retaining a scrappy, amateurish edge thats remarkably endearing. The latter two, despite their move into big theatrical power-pop, are still also very strong albums, with pop hooks basically coming out of their arses, and its no wonder the band became as popular as they did with The Black Parade, and deservedly so.
I think its a real shame that they never really achieved any sort of credibility beyond commercial success and the pages of Kerrang, because they really deserved more than just being written off as "that band that 13 year old goths like". So yeah, I've rambled enough now, point made.