I presume with log off you mean hibernate or similar. MIne turns the monitor off after 30 minutes.
This is for XP, rightclick anywhere on your desktop and select properties and then the screensaver tab. On the bottom you'll find the power settings. Press the power button and you can configure your computer to do anything you like except make you a cuppa tea. Note some of the custom settings may suit you better. If you want to be in complete control set everything to 'never'. Have fun.
Remember though that you are increasing the risk that somebody else can access your computer while you are away. That's why the default is what it is - to protect you from bad people.