Is using Wi-Fi safe with a home connection?

I'm connected to a Wi-Fi connection with my iPhone 3GS. I have a doubt that on other end my relative seeing all my personal content. How it is possible. I'm deleting all my history in phone As soon as possible

If your wireless network is protected by a password you should be fine.

Unless this is a secure connection yes they can possibly read every packet including clear text user names and passwords. Only use secure router connection or a local criminal can also do so. The history of your phone is not visible from outside.

Raj, if they have access to the router they can see everything, but if you have access to another computer off the network you can setup an SSL/VPN tunnel to that computer and all your traffic will be encrypted. There are alot of free proxy servers that offer free ssl connections to them, but make sure you don't do any online banking while connected to them.

You say "on other end my relative", which implies that you have some sort of messenger service running such as Skype. There should be settings in the messenger service that allow you to configure how others can access files on your device.

You should also make sure that you have good encryption on your Wi-Fi network. WPA2 is the best encryption for home use. Note, however, that anyone on your internal network (Wi-Fi or Ethernet) can reach your phone, but should not be able to access your files if you have set the phone's security settings correctly.