If you are worried about the security of your email, the only way to have some reasonable confidence is to manage the encryption yourself, using something like PGP/GPG. Some points to note
When using a web client, https only encrypts your communicaiton to the mail service you are using. It provides no guarantee regarding the level of encryption which occurs during the message transport process which occurs between the servers
Some SMTP servers do support TLS etc if asked to use it. However, there is nothing in the SMTP protocol specification which requires them to do so. Many SMTP servers don't provide it.
You have no guarantee regarding the mail servers a message will be passed through. Many people think that when you send a message from server a to server b that the message is always passed as a direct connect between those two servers. This is not necessarily true. The SMTP protocol was designed at a time when networks and sesrvers were far less reliable than they are now and when many places did'nt have direct connections to the core network. To enable reliable mail delivery, the protocol supports mail relaying. In simplistic terms, the sending mail server can say "Hey, I've got a message for gmail, but I can't seem to raise him and I have to go and upgrade my kernel, can someone pass this message on for me when he returns? I would do it, but I have to go an upgrade my kernel and won't be around for a while". Another, possibly previously unknown server may respond saying "Hey sure, I am an MX host for your recipient domain, I can relay the message for you".
While all of this means that email is usually fairly robust, in the sense that mail sent to a legitimate address will usually get delivered successfully or bounced back and rarely just vanishes, it does create some weaknesses in the protocol which expose the system to a number of exploits, such as DNS spoofing. Even if you ignore the transport aspect of email, there is also the issue that messages are routinely saved on servers unencrypted, such as in mail spool directoires, making them readily accessible to anyone whith sufficient access rights on the server. Even forgetting that, how many of the people you have sent mail to actually store or archive that mail in an encrypted secure manner? If I sent you a message with sensitive data in it, do you encrypt it before storing it in you mail archive? No? So what happens to my sensitive mail message when you computer is infected with a virus or malware? What control do I have over this sensitive information once I send it to you?
Email infrastructure was designed at a time when security was not a high priority. The huge growth and the desire to keep everything working and the need to maintain backwards compatibility means that many of the enhancements which have been introduced, such as encryption of communicaiton between servers etc is optional and therefore cannot e guaranteed and although there have been many improvements, at the end of the day, you have to consider email as an inherently insecure communicaiton channel. Unless the sender and recipient take additional action to increase the security of email communicaitons, you should consider the message as being insecure, even if you believe the companies maintaining the servers involved are reputable and apply good practice.
We should also keep things in perspective. How much of the mail you send has any information in it which is really sensitive? Of what real value is this information to someone else? How easily could someone get this information and is the cost of doing so less than the value obtained? Security should rarely be considered in terms of is it secure or insecure. The question should be is it secure enough for the purpose I am using it for. Is email secure enough for my Christmas greeting I send to my grandmother? Almost certainly. Is it secure enough for my bank to send my account access code or PIN? Definitely not. Are there ways to increase security of messages? Yes, but they all come with a convenience cost. For example, PGP/GPG and encryption of your message. They provide additional good security, but decrease the convenience of communicaitong by email. Now you have to create and manage encryption keys and your recipient needs to setup their client to use your public key to decrypt your message before they can read it. If the content is sensitive and valuable enough, this increased inconvenience may be worthwhile.A lot of the time, it isn't.