If you want Google chrome to remember your password for each website you use daily, most of the times chrome asks for that. But in some cases it doesn't ask for save passwords.
If you want your chrome to remember all passwords, you can choose an addon of chrome Autocomplete= on
Add this to your chrome
You can also do this by given trick
you can also import all data stored in your firefox browser. So use firefox for login into all accounts you want to remember and save its data in firefox when it prompts, Then import all saved passwords in Chrome. Now use chrome and it will remember your all passwords