If your mobile device is asking for password then its means that the Wifi-router from where your mobile is receiving the signal is password protected. Without entering the password, you will not able to access web through wifi.
Also if for some reason DSL or Broadband provider changed your password, look for wifi on your phone without the lock symbol, you can connect to these without a password, but it's not a secure connection
Neither is WEP. No modern routers/modems use WEP by default. If you've set it to WEP yourself, quite frankly you deserve someone to steal your internet.