There is a whole host of programs of all sorts. I think Iceland is quite popular for such things. What kind of exchange are you thinking about and from where in the world.
Lots of exchange students from Europe come and study in the University of Iceland via the Erasmus program.
Nordjobb is a work exchange program for young people from Scandinavian countries. Especially in the summer time.
AFS and Rotary are big in exchange programs all over the world and AFS in particular is big in Iceland.
You can always go straight to the source and just enroll in the University of Iceland by yourself.