Anything relating to income tax for seven years. Everything else (utility bills etc.) no more than a couple of years. Receipts for expensive purchases for three years or so in case you need to take them back.
What British Red says. I keep the annual statements of interest from places like banks but shred the ongoing statements after a year or so. If you have other investments again the ongoing valuations aren't important, what the tax man is interested in is income and profits/losses.....
Be ruthless, at least a bit. I've recently dealt with my father in law's paperwork after his death and it was clear that most of the stuff he kept as "important" really wasn't - but it took another eye to see it....