If after entering username and password and clicking the button "Login" the browser offers to save the password (by displaying a dialog box or strip under the address bar), select the option appropriate to ban keep (i.e. don't save). Some browsers also offer the option to stop the output of such a dialogue on subsequent visits to the same site (as a button "Never for this site" or similar). Then select this option.
Such requests do not appear ever while using as mail services, and any other sites that require authentication, disable browser remembering the password. A way to disable this function depends on what browser you use. For example, in the desktop version of Opera: "Settings" - "General settings" - tab of "Form" - uncheck "Enable password management". Mobile browser UC to turn off remembering passwords: Settings - Preferences - Security tab - Never Save in the Login Record.
Remembering the password can also be carried out in cookies. To avoid this, when you enter account settings select the "another computer" or "don't remember", or uncheck "Remember me" (depending on what you use e-postal service).
When finished with the mail, be sure to click on "Exit". If this is not done, long-term omission of output can occur automatically, but is not guaranteed. Moreover, auto output is not provided in all postal services.
In case you forgot to turn off password saving in cookies, delete these files manually. It's not necessary to look for the folder where the browser stores these files. Remove them and the browser itself. For example, in Opera: "Settings" - "Common settings" - "Advanced" tab - item vertical list "Cookies" - click "Manage cookies" - select the desired website in the list is the "Delete"button.