Depends on the receipt. Donations, we keep. If it’s an online thing paid with a credit card I suspect the credit card statement would do, but I’ll usually print out and keep whatever electronic receipt they issue anyhow.
Medical: Well, except for one year where we were able to deduct about a thousand dollars, it’s not been an issue, but for the most part, our payments (checking history and/or credit card) are the only really reliable source, what with a lot of the expenses being run through our flex spending. A simple EOB wouldn’t say whether we’d paid and been reimbursed, or paid out of pocket. So for that, we rely on a report from the relevant accounts in Quicken, showing outflows, insurance reimbursements to us, reimbursements from flex spending, and the net amount we really were out of pocket. If we need a cancelled check as proof, we could print that when we do the tax return. Other backup for that report would include the credit card statements (soft copy readily printable), and a printout of flex spending transactions from the servicer (ditto).
Other deductions aren’t receipt-able - charitable and medical mileage. To document those, we go through our calendar (Palm Pilot in our case) and list all such trips, and their distances.
Basically, when tossing receipts, you have to apply some knowledge of what they might be needed for, and any special circumstances (like the tax credit mentioned above).