Benefits of allow the browser to save the password:
- Spoof websites are more easily detected because the username and password don't show up (this may be a mute point if the username is saved but not the password).
- Keyloggers won't pick up the password if you don't type it. (Thanks to Thrawn)
- People will be less likely to keep the password in an obvious place (i.e. sticky note)
- Stops someone with access to your computer from accessing the passwords (the level of access needed can vary based on how the passwords are stored).