As far as cheap/discount tickets:
Steppenwolf has the RED card program for anyone under 30. Pay $100 and get a card that can be redeemed for six tickets (<$17 a ticket) - you can use all six at once if you want, see a show solo six times, bring a friend three times, etc. Companions do not have to be under 30 as long as the RED card holder is with them. Card can be recharged $100 at a time but expires on your 30th birthday.
Chicago Shakespeare sets some seats aside for anyone under 35 - they're usually in the second or third row along the side of the thrust stage. Very intimate view, great value for only $20. I kicked myself for not trying it earlier.
Goodman sometimes sells the last few rows of the mezz for 50% off plus a drink discount if you're under 35(?). They also sell mezz 50% off for same-day performances, IIRC.
Broadway in Chicago used to limit same day rush to student/military (which kept me from seeing a lot of shows unfortunately), but the recent Rent and Aladdin tours opened rush to everyone. As someone that's still saving up to afford the grad school application process, I really hope they keep it that way for future shows!
I think Joffrey Ballet also does a student rush or discount, but I don't know specifics. Lyric Opera does a 50% off rush for anyone starting a couple hours before a show, but that price is still too rich for my blood so I've never tried it.
Hottix.org sells 50% tickets thanks to the League of Chicago Theatres. You usually don't get to pick your seat (depends on the show). Today Tix and Goldstar also operate in Chicago.
I'm not familiar enough with the smaller theater companies to know if anyone else offers discount programs.