On the other hand, if you're using an app like Facebook to log-in into your account, then it is not possible to save your password. That said, there are some apps on Play Store where you can save your password safely, if you've issues remembering them. read more
There is no functionality to view saved passwords included in the stock browser. The only method for retrieving passwords saved in the stock browser is to open the webview.db file (it's an sqlite database) in /data/data/com.android.browser and look at the password table (it's stored in the clear, no encryption or anything), but that requires root. read more