The Wisconsin Union holds free music concerts - the dates of which vary (check out their website below). The shows are fun and lots of people turn up. Good place to go alone, with people or to meet people.
Some of the events have regular days. Every Thursday at 9pm is Open Mic. It's often hilarious to watch and sometimes you can be a little shocked at how good people are. Mostly musicians, a few singers and throw in a comedian once in a while. Any one with a student ID can get up to perform whatever they want for 15 minutes. That's always in the Rathskeller on the first floor.
Generally on the weekends bands play from 8 until midnight. Some are local, some aren't, but they are always good and you can't beat free. Bands such as Little Blue Crunchy Things and Cork 'n Bottle Band have played here before. I love during the summer and into the fall when the music's outside. I have so many memories of sitting by the lake and listening to a good band, drinking a good beer. The beer lines are insane though. (if you go downstairs by the pool tables, they sell beer there too. no one really knows that... it'll take about 5 minutes to get something as opposed to 20) You usually have to have a student ID or Union membership to buy beer.
The entire organization is run by volunteer students and alumni. Most of the events are free and if they're not they're usually under $5.
Check out their website for current listings:
Memorial Union - Music Committee
side note: the Wisconsin Union was the first and only one of a handful of campus unions that allow liquor anywhere in it or outside
another side note: the Wisconsin Union actually holds a copyright on the coloring scheme - the infamous orange, yellow and green chairs - no other union can copy it...