I've just moved to London, as I've just started at uni here. At our freshers' fair, I was given quite a few leaflets to do with cheap/free tickets, and I just thought I'd draw attention to the various schemes.
Obviously, it helps if you're a student, because just asking for a student discount at a concert or theatre makes you seem eager, intellectual and to be pitied. However, when a little more than flashing the NUS card is required, there's always the FreeB scheme at the Barbican - join up, (for free, naturally) and look around to see what they have free tickets for. It's for 16-25 year olds. (Much like the 'A Night Less Ordinary' setup for discounted theatre tickets - also worth a look.) The good thing about the Barbican, though, is that it's not just one medium or genre. There's film, theatre, music, dance etc.
Another ticket scheme worth a look is the Royal Opera House 'Student Standby'. Sign up, and you'll receive emails about tickets for the opera or ballet that are spare and are on sale for the heavily discounted price of £10. Student ID is required, but this is a great plan to get in some culture for cheaps!
As is my last leaflet, with the English National Opera. Called "Access All Arias", membership is once again free and fixes prices at £30 for stalls, £20 for the dress circle and £10 for the upper circle. Again, very discounted, but that's not all. You also get a discounted +1, and if that wasn't enough even the programmes are half price.
All of these things can be Googled, and if there are in fact any other students in here other than myself, can I just say - just because these things are in London doesn't mean there aren't other schemes in other areas. These are just examples. Apparently a huge number of theatres and concert venues are now offering last-chance tickets to students at ridiculous prices, as long as you're quick.
Check it out

