Bank statements, as far as I'm aware, are only available online for about a year
I think you're legally supposed to keep them for 5 years.
I keep water bills, so we can compare them, but gas and electricity are now just done online; there is a complete record of those online though. We don't often use credit cards but when we do the bills are kept till they're paid.
Receipts though, for anything electrical for instance, anything with a guarantee, are kept in a file with any relevant instruction books. I go through it every now and then to get rid of any long gone.