I had posted this awhile back in response to the exact same question, by Maribel, so I'll re-post it. If anyone has anything else to add feel free because I most likely missed some stuff...
Here's a little something I came up with off of the top of my head, It's kind of long so bear with me.
* Dives w/ Live Music *
http://themutinychicago.com/ - Big sign painted on their window "Bands Wanted" so there's always some kind of band playing here. Sometimes you get lucky and the band is alright, other times you won't and they'll suck.
http://www.drinkatcalsbar.com/ - My personal favorite, small, dirty, and cheap. Could you ask for anything more? When there are bands the cover is usually $5, so if they're terrible you don't feel as cheated as if you payed, say, $10. The bands play right on the floor so it has that old school, basement punk rock show vibe.
* Just Plain Dives *
http://www.yelp.com/biz/two-way-lounge-chicago-2 - Really weird mix of people (Gangbangers/Hipsters/Old Drunks) but still recommended.
http://www.whirlaway.net/index.html - The bartender Maria is a total sweetheart. Protip: As tempting as it may be do NOT, I repeat, do NOT sit on the sofa. OK jukebox.
http://www.yelp.com/biz/l-and-l-tavern-chicago - They serve absinthe here and have a good jukebox. However, sometimes it gets overrun with annoying college students who are "slumming it".
http://www.yelp.com/biz/innertown-pub-chicago - A little divey oasis with a decent jukebox tucked away in a residential neighborhood. Got thrown out of here once, but I don't hold that against them.
http://www.yelp.com/biz/olas-liquor-chicago - Ahhh Ola's, what can I say about Ola's, Well it's small, the owner is Polish so you can never be sure if she's insulting you or not, and I once saw a man drink a flaming shot of Yukon Jack out of his glass eye here. I think it's safe to say that I love Ola's. You get the feeling that this is where Bukowski would drink.
* Semi-Respectable Drinking Establishments *
http://www.californiaclipper.com/ - Pretty cool bar. They play mostly Rockabilly/Country/Blues. I got thrown out of here once too, ahhhh good times. No cover so that's a plus.
http://www.myspace.com/liarsclub2006 - Cock Rock/Metal Bar Tolerable in very SMALL, and I mean REALLY small, doses.
http://www.delilahschicago.com/ - What was once the jewel in the crown of Chicago Punk Rock dives has now become a caricature of it's former self. I don't know if it's the Lincoln Park Chads & Trixies, the liquor snobs paying $30 for a glass of scotch and $10 and up for some obscure microbrew, or the nightly poser fashion show with outfits supplied by The Alley, but I totally hate this place now. If you've never been I suppose you should experience it at least once.
* Not worth your time or money *
http://www.exitchicago.com/ - The Exit is dead to me. Avoid at all costs. For all of the reasons I hate Delilah's I hate this place even more. It's like the Punk Rock episode of Quincy brought to life.
So there's my suggestions, brought to you by many years of black outs and behavior that had me apologizing to my friends the next day. Hope it helps. Cheers.
