When my paid developer membership runs out with Apple, what happens to my existing apps on the app store?
I know that I cannot add new apps then, but do my existing apps stay? Can I change prices? Can I get paid for sales? Can I update those apps? (Am I missing any questions here?)
One important addition to the previous answers: your apps will NOT be completely removed by Apple, so if you renew your membership later, they will return in the App Store within 24 hours. You do not need to resubmit them. Please note that this doesn't invalidate the other answers, but I thought it was worth mentioning.
What happens to my apps on the App Store if I do not renew my membership?
If your membership has already expired when you renew, your renewal will activate once you complete the renewal process and any free apps you had available for download will become available again within 24 hours. Any paid apps you had available for download will become available again after you sign in to iTunes Connect and complete your Paid Applications contract. You do not need to resubmit your apps.