Record-keeping question - how long to keep receipts and credit card bills?

I was doing some housecleaning today between football games, and ran across some bags and boxes of stuff that I have been storing for a long time.

For example: I keep all my paid credit card bills, organized by year. I found a box of them with bills that I paid back in 2007 and 2008; later I found another box with paid bills from 2011 and 2012.

Of course, I keep my tax returns forever. But this question is about bills that I paid, not tax stuff.

Do I need to keep these? How long? When I do my 2016 taxes in a month or so, is there any reason to keep my paid bills?

How long do you keep yours?