If you use Google Hangouts or even GTalk (earlier) or any instant messaging tool to chat using Google’s service, then your chats are all stored by Google. You can access them by logging into your GMail / Google Account.
Once you log in, on the left pane, you will see Inbox, Important, Sent Mail, etc. and the last option there will be More.
Click on More, and you will then see further options Starred, Chats, All Mail.
Click on Chats and you can see all your saved chats. You can also delete all the saved chats. By default, Google saves all your Chats on it’s servers.