If you log in to a site using your email address, you will still be able to log into that site. You just won't receive and emails from them as it's just a user name (like you use John Boy) to log in here.
Some providers allow you to keep your email address, but they normally make a monthly charge for the privilege.
Best bet is to find a free supplier like hotmail, but these often have no spam blockers and are bombarded daily with junk. My hotmail account gets on average 20+ junk emails a day, while my BT address only gets around 1 per month, normally telling me a USPS or Fedex parcel couldn't be delivered

. My gmail account (so far) has never received any spam/junk