I would like to have my iPhone 4s (ios 7.1.2) to ask me to enter my email password every time I use the iPhone standard email app. I don't want the iPhone to save the password for security reasons. Is there a way to do this?
What you're asking for is not possible with the built in Mail app, afaik. If you want to enter your password every time when accessing the account/s, you'll have to use a browser to login, if that's possible.
The Mail app will remember your passwords. When you add an account, you have to enter it, or else you can't set up the account.