If no one else here has mentioned them, I'll give a big shout out to the New Pornogaphers as well.  I haven't heard the new album yet but I'm fully confident it's brilliant.

Also, if Gogol Bordello's touring in your area, you probably want to catch them.  Dengue Fever, too.

I would be remiss if I didn't mention having seen 31K in a coffee shop, and having watched the lead singer belly crawl into the crowd, take his clothes off, change into a WWII pilot's dress uniform, then end the show as soon as he had the last button buttoned.  It was a rapturously moving experience, but only to pilots.

Mogwai is a band that continues to blow my mind.

I just got the new Aesop album but haven't listened to it yet, is it good?

I'm really glad that a lot of radio stations have been playing all this Max Roach since he died. Getting the word out and such. He was one of the great jazz drummers of all time, and not too well know amongst the general public. Cool you've been checking him out. For anyone wanting to hear some of his wonderful music, 'Max Roach Live At Basin Street' with the legendary Clifford Brown on trumpet, and 'Max Roach +4' are good places to start.

Those bands are not "original" emo bands.  The term emo was a derogatory applied to Rites of Spring (Guy Piccioto's band pre-Fugazi), and referred specifically to playing hardcore-influenced music from a personalized, rather than politicized, standpoint.  There are a ton of absolutely amazing late '80s emo bands, from whom only ATDI really takes any influence--Moss Icon and Nation of Ulysses come immediately to mind.

The term then sort of mutated in the early nineties to apply to the San Diego/Bay Area "spock rock" scene--including the Swing Kids, who gave rise to the Locust (there's also, oddly, a ton of bleedover between the SD hardcore emo groups and Rocket from the Crypt, who are more or less the definition of Not Emo [or Notty Mo]), and Mohinder and Angel Hair in the Bay Area--all of which was labeled "screamo" when "emo" went mainstream, as well as the not-quite-pop-punk Bay Area bands like Jawbreaker (who begat Jets), Avail (who spiritually begat HWM), J Church (who begat nothing but are still around).  

Both the SD and SF/Berkeley bands really started mellowing out their sound as the nineties went on, leaving the door open for SDRE (who were only considered emo retroactively, they were part of the Seattle indie scene) as well as the load of absolute crap that Polyvinyl and Revelation released in the late '90s (Lifetime, Braid, Joan of Arc, Elliot, I'm forgetting a bunch but who cares) which really laid the whole "boys with mascara tear tracks," curse on the sound, and led to what's now called emo.

The hilarious thing is that at every step of the evolution, everyone who was into the "old" emo disavowed the "new" emo, and claimed they listened to the "real" emo.  As you are doing.  As I am doing.  As every good music snob worth her/his salt will continue doing until North Korea nukes us all.  As I have just finished doing to you...

Thus endeth the lesson.

But here's a list of inspired recommendations...

If you like ATDI, try Moss Icon, Jawbox (I believe ATDI covered "Savory" at one point), and of course Fugazi.

If you like Appleseed ("Februrary," is probably my favorite single song of the past year, although it's totally unrepresentative of the album), especially their more technical stuff, you should definitely check out the mathrock mob--Rodan, Hoover, Slint, June of 44, etc.