These days a lot of receipts are sent or displayed electronically. A great way to archive your receipts is to save them to PDF and place in a separate folder on your computer. On a Mac this is very simple to do: File -> Print… -> PDF -> Save to PDF. On Windows, you’ll probably need to install 3rd party software such as CutePDF.
Also, saving your boarding passes to PDF when you check-in online is a good idea as well, especially if you don’t have a printer you can connect to at that specific moment. Not only that, it’s handy when you need to show proof when your frequent flyer mileage doesn’t post to your mileage account.