All modern browsers include a “Remember password” option while logging in to websites. I recently switched to Google Chrome full time, and one issue I noticed was that it sometimes refuses to save passwords, only on particular websites – ie. you do not even get the prompt to save password.
This is, no doubt, a major inconvenience, as you have to enter login details every time you visit such sites. This is usually caused by a form tag attribute autocomple set to Off.
How to force save passwords on Chrome
Install Toggle Autocomplete On userscript.
If you use an older version of Chrome that does not support userscripts, use Autocomplete = On extension that manually overrides autocomplete directive and makes Chrome remember passwords.
But it would be advisable to upgrade Chrome (for security and performance reasons) and get the userscript. Userscripts consume far less memory than extensions, which consume more RAM (as they run as separate process).