Just a random question I've suddenly thought of- does anyone know what happens to an Olympics stadium once the event is over? Is it kept for future sports/recreational events, or taken down?

Okay they reuse and everything but only for special things.

It depends, some stay the same and are used for the original sport and some are altered, the track stadium in Atlanta became a baseball stadium.
The track stadium in Beijing is now used for soccer, but they retained the track so track meets could be held there in the future.
The one in Barcelona is used for soccer and American football.

the birds nest will be used for other recreational events because they already spent so much money on it

Depends. Some become concert halls. Some become sports stadiums (the Beijing National Stadium will hold it is soccer team). Very often smaller venues (like Galatsi Olympic hall in Athens) r not kept forever. Galatsi Olympic Hall has been bought from the government & will be turned into a shopping mall.

Most of Beijing is sports venues (except for things like the triathlon & archery courses) were created to be permanent structures. The Aquatic Hall (''the water cube'') will be used for aquatics & the national indoor stadium will be used for indoor venues.