No rules that I know of about keeping them. A couple of years ago on a training session (run by an LA Advisor) it was suggested that we take the front cover off last year's Maths papers and then give them to children for them to identify the mistakes/misconceptions.
No school I've worked in has had the space to store papers for more than a year - they stay in a cupboard until next year's papers come back and then they are shredded to make room for them.
Thanks guys, an interesting range of opinions! Last year I wanted to go through ours as a subject leader but discovered by accident that they had been shredded by the end of term. It just seemed a little quick to me!
We keep ours initially to check for marking errors, then in case a subject leader wants to do an analysis. At my current school they are kept forever manly because nobody ever bothers to throw them out.