I'm pretty sure Brewski's is my favorite dive bar. Definitely in the South Side, possibly in the whole city. I spent so many Friday nights there when I was younger that part of my love could be just because I have such fond memories. Even when it's packed, it's still a good time. I'll be gone for years and the bartenders still remember me when I return. And you can't beat the prices.
Don't go if you hate crowds, though. This place will get packed. But if you think you can handle it, don't be afraid to go to the back. There are tables with more space to move around that people either forget about or don't know are there. Standing around the bar can get annoying with people walking back and forth so I'd recommend working your way to the back and setting up camp there. You can still get the bartender's attention from the far end of the bar. An added bonus: you'll be closer to the awesome jukebox.