There are numerous alternatives to GMail, but no so much that care about privacy. You may have heard of Lavabit that was used by Edward Snowden, but sadly it’s now closed.
Hopefully others have created similar services, that offers good privacy, among them there is:
This service is still in private beta and requires an invitation. But you can already reserve your address today and that will subscribe you to the waiting list.
This is a very promising service, offering end to end encryption using PGP and will also support intermail and DarkMail (from former LavaBit and Silent Circle developers)
Another alternative is ProtonMail, which also offers end to end encryption, but is also in beta and require invites.
Note that I didn’t test LavaBoom and ProtonMail yet (I’m still waiting for the invites), but I’ll report on it once I get access to them.
This service is available today and doesn’t require invitation. It also offers end to end encryption using a password you assign to your recipients. This way you only have to communicate a password to each of your recipients and they can read the mail.
Of course you also have the choice to not encrypt mails (and it can be set like this by default).
Note that Tutanota is fully open source.
But if you don’t care about encryption, you have other alternatives like ZohoMail (https://www.zoho.com/mail/) and if you are not afraid of Microsoft or Yahoo, you can also use outlook.com and yahoo webmail service of course.
These are only few examples of GMail alternatives, there are hundred of existing webmail services you can choose.
You can also choose, like I did, to make your own mail server. I’m personally using my NAS network drive as my mail server with my own domain name. But of course for that you need to be a little more geeky 😉