it is possible. Depends on where you would like to encrypt them: locally or on the web servers.
Have you heard about PGP/GPG before?
GPG is an open source free version of PGP. The GNU Privacy Guard - GnuPG.org
Wikipedia info: https://en.wikipedia.org/wiki/Pretty_Good_Privacy
It's available for almost all platform, if you have Windows OS worth to try is GPG4Win.
In short PGP/GPG uses symmetric key cryptography.
First you have to create your own key (public and private key).
Your public key is for people who will email with you - they have to know what your public key is, because they will use it to encrypt message for you.
If you want to send encrypted message to other person then you will need their public key and your private (secret key).
It sounds complicated but in practice it isn't.
Here are some tutorial vids you will be helpful I hope: GnuGPTutorial - YouTube
Above example is how to encrypt your email/files locally, but there are also webmails which offers this feature - they do all this work on web servers like: Countermail or HushMail - however I don't know how much they are reliable and secure since everything is hidden for end user.
I'd recommend to use PGP/GPG encryption on your own computer if you have time to learn it. It's easy in fact but needs few minutes to understand how it works.
Setting up GPG, and learning it, would be next...but you will never get all
your contacts to use it. Unfortunately.