I put them in a box, and every now and then, go through them and bin the ones which won't be needed, i.e, groceries already consumed, tanks of petrol, things which won't have a longer-term guarantee. (In theory, I do this weekly; in practice it's when the box is over-flowing...)
I do go through my bank account a lot more regularly, so sometimes I have to shuffle through the top layer of receipts to check one I don't remember. This has meant a couple of times, I've called the bank or credit card company in question to query an entry. This was fraud in one case, but in another, it was something I'd bought, but the name on the credit card bill was different from the company name I'd brought it from. No wonder I was confused, but after querying it, it was something I accepted. I have since had at least one company inform me that, "it will appear on your bill as this name", which makes me suspect I am not the only person to have been confused by this sort of thing. (It was good to be warned upfront, though.)
Receipts for things like new household goods (e.g. washing machine or PC printer) are usually attached to the inside of the relevant manual, on which I'll also write the serial number. Said manual then goes in the drawer that contains that sort of thing, and I probably won't look at it until something goes wrong or I'm having a tidy-up of that drawer.