For an itemized deduction on Schedule A for non-reimbursed qualified medical expenses -- should the IRS ask for supporting documentation -- you would need something proving amounts actually paid. An insurance EOB may show what you were responsible for, but that is not in itself a proof of payment. However, coupled with a credit card statement showing an amount & payee, then it would be helpful.
You wouldn't necessarily need an individual receipt for every service; an account statement showing payment for all services during the year from a particular provider is acceptable. As are printouts from your local pharmacy for prescription amounts paid throughout the year.