Can i disable history being stored on safari?

Yes, this is possible, and very easy. Before you do this, clear your history in Safari and quit.

Navigate to ~/Library/Safari
In that directory, you'll see a file named History.plist; Get Info on it and check the box labeled "Locked".

You're done. Now when you surf the web, Safari will temporarily write the history to this file, then erase it when you Quit.

Mulder

Firefox can be set to remove all private information when you close the program. Depending how you are connecting to the internet, removing the history trail might be useless anyway, as many routers keep a log of sites visited.

Private Browsing is a good way to prevent items from being stored in the History. It will remain switched on until you quit Safari, so you need to remember to enable it each time you launch the application. There's no other way within Safari to block items from being stored in the History.

Alternatively, you can use a 3rd party utility to alter the "inaccessible" settings. For example, Onyx allows you to set the number of pages stored to zero.

Hope this helps...

Have a look at TinkerTool:
http://www.bresink.com/osx/0TinkerTool/details.html