The following is a list of email services hosted in hidden services to send and receive anonymous email through Tor.
Always remember that you will not have a clue about who the administrators are. It might be the NSA, a scammer, someone without technical competence or someone wonderful who really cares about your privacy. Trust nobody, email messages should always be encrypted using your own private encryption keys.
CTemplar (http://ctemplar42u6fulx.onion/): An Icelandic email provider that does not log user IPs and has PGP encryption. You can create an account without providing any identifiable information using their Tor .onion site or the clearnet, there are free and paid options.
Cock.li (https://wwwcocklicdexedh.onion): A free email and XMPP anonymous service funded with donations that allows registration with Tor , VPN and proxies. There are over a dozen domains to choose from when you sign up for a cock.li email address.
Secmail.Pro (https://sigaintevyh2rzvw.onion): Free email provider with anonymous sign up and PGP encryption, the service is widely used by various dark market users. Unfortunately it can not receive email from Gmail, Yahoo and other major providers as their servers are marked spam, Secmail claims to be working on a proxy system to solve this.
ProtonMail (https://protonirockerxow.onion): Fully encrypted Switzerland based privacy email provider, it can be accessed in Tor but signing up must be made in the clearnet and if you are using a VPN or Tor you might be required to verify your mobile phone number with a SMS message, the company claims this is to avoid spam.
Mail2Tor (http://mail2tor2zyjdctd.onion/): Free anonymous email service with webmail (SquirrelMail), POP3, IMAP and SMTP. It can send email to addresses out of the Tor network using relays, no important logs or emails are stored in any of those servers in case they are seized, they only contain Tor and mailing software, user data is stored encrypted in a hidden Tor node which IP is not known.
Tormail.io (http://bitmailendavkbec.onion/): Anonymous email provider with servers in Sweden and Switzerland, they do not keep any logs, PGP encryption is integrated in their email services, it can be accessed via webmail. This is a paid service, payments made with Bitcoins to maintain privacy.
Elude.in (http://eludemaillhqfkh5.onion/):With personal data encrypted in the server and end to end encryption, it has the option to permanently delete the account in case of an emergency. Signing up with Elude.in only requires you to pick a username and a password, the service is free but making a donation will increase your inbox quota and number of aliases.
DanWin1210 (http://danielas3rtn54uwmofdo3x2bsdifr47huasnmbgqzfrec5ubupvtpid.onion/): Personal website providing free anonymous Jabber and email account that can be accessed in the clearnet or Tor.
Guerrilla Mail (http://grrmailb3fxpjbwm.onion/): Disposable email address with Tor access, ideal to receive registration email details or brief communications, you can reply using the interface but emails are only kept for one hour.
TorBox (http://torbox3uiot6wchz.onion/): Hidden email service only accessible in Tor. What makes this email provider different from others is that you can not send or receive messages outside the Tor network, it only works if you communicate with other people using a .onion email provider.
How to access Tor? For serious security you must install the official Tor browser but if you are not too concerned about tracking and anonymity, you can download the Brave browser, this privacy browser is able to access .onion sites and Tor.