Yahoo! Messenger has the archive feature and it gives you 3 options to handle it.
option 1 , Yes save all my messages
option 2 , Yes save all my messages, but clear theme each time I sign out
option 3 , No, do not save any of my messages
This options important if you are at public computers like school , internet cafes
How to see which setting you have
- Sign in to Yahoo! Messenger
- Hit Messenger tab and click on Preferences
- At left side click on archive and check your archive status at right side
You can view or delete all of your archive from there 
If you just want to read or reach any chat archive ,(from main Yahoo! Messenger window) right click on your friend name and click on Message Archive.
Where are that archive files on my computer ?
C:/Windows/Program Files/Yahoo!/Messenger/Profiles/your user name/Archive/Messages/your friends user name/ . In this file u will see 1 or more files like 20070618-your_user_name.dat this means which day you chat with your friend.