You can perform a factory reset on your iPod Classic without iTunes, but only the settings are reset. No music or videos are erased from the device. You will have to still connect the iPod to the computer to delete all media files. But if you are an iPod Touch owner, then you can do a full factory restore that resets the settings and erases all content.
A factory reset on the iPod means the settings are set back to the default options it came with. Factory resets retain the media files you have on the device, so they will not be deleted when you reset. This is the safest way to troubleshoot a technical problem while keeping your songs and videos.
A factory restore is when you restore the device back to the original settings and erase all media, just as it came out of the box when you first bought it. The iPod Classic does not permit a factory restore without iTunes, but the iPod Touch lets you complete a full restore from the device.
You can perform a factory reset on your iPod Classic by going to the "Settings" menu and scrolling down to the bottom. Then you would select "Reset All Settings." The music player should reboot showing the Apple logo. The reset process may take a few minutes, but once finished you'll have the default factory settings with your media intact.
On the iPod Touch, you can do both a factory reset and a factory restore, depending on your preference. If you do a factory restore, you will lose all media including your apps and data. To do a factory reset go to the "Settings" app, select "General," tap the "Reset" button and then choose "Reset All Settings." In the same area, if you choose to do a factory restore, you'd pick "Erase All Content and Settings" instead.