Yeah as xTanyax says We Will Rock You deffo do have standby student tickets for £20 the day of the performance. They are normally really good ones - last time I got one i was right in the centre of the stalls! If not I'm sure there would be day standbys on the door as I doubt they fill every seat on Monday-Thursday performances.
Mamma Mia! doesn't do any type of reduction in tickets as the show is so popular. My suggestion is that you try for a Upper Circle seat or possibly combine a visit to the theatre with a student weekend in Bristol. The International Tour of Mamma Mia! is on at Hippodrome between 30 November 2007 - 2 February 2008. Top price seats are £30 and ones right up in the Upper Circle are a tenner so deffo a bargain to be had there! I saw the tour last Christmas in Manchester and it is just as good as the London production. See
www.mamma-mia.com/bristol/bristol.asp for details.
I'm not sure about Chicago but I'd imagine they also do some sort of day tickets - also as already suggested -
www.theboxoffice.com has loads of summer offers on tickets at the moment. Best price Chicago tickets are £25 which is quite good. If you do go when Kelly Osborne is playing Mamma Morton - do say what she's like cos if she's good I may even go again!
Good luck!