If the answer is yes to either of the above questions, then you probably know that you can't do that easily as Apple have formatted the iPod media storage in such a way as to hide the music and video from other files and photos, rendering it invisible. Assuming you sync your entire library, then your iPod is a full backup but, while you can mount your iPod as an external drive, you won't get access to the audio or video files. Well, actually you can if you use one of the free utilities listed below.
NB: If all you want to do is to relocate an existing iTunes library, then you can find detailed instructions from Apple here, although they do require that the old storage is connected to whatever system is hosting the new location and that your iTunes music folder is set to be kept organized. If your're moving the database to a completely new system and/or your music folder is not kept organized, then you might find the instructions on Jilles van Gurp's blog more useful. Also be aware that if you have any DRM protected tracks, you'll need to de-authorize the old system and then authorize the new one before you'll be able to play them.
There are also other ways to view invisible files and folders to access the music files but they involve changing global file system settings, which could present some users with more than they really want to see. The Kirkville blog has an excellent article on how to do this on Mac OS X and Windows so if you're happy dabbling at that level, otherwise…
YamiPod is a freeware application to efficiently manage your iPod under Mac OS X, Windows and Linux. It can be run directly from your iPod and needs no installation.
It automatically recognizes your iPod, you can copy mp3 and AAC files to and from the iPod and you have read/write access to mp3, ID3 and AAC tags. It has a built-in music player and supports playlists. It can also export and import lyrics, tracks and playlists, remove duplicates, find lost music and can sync with the iPod.
It can even add and edit notes, news and podcasts, display iPod information and repair a faulty iPod.
Floola is a freeware application to efficiently manage your iPod or your Motorola mobile phone (any model supporting iTunes) under Linux, Mac OS X and Windows. It can be run directly from your iPod and needs no installation.
Floola can copy, add and extract songs or videos to and from your iPod, find duplicate tracks and search for lost tracks, playlists can be managed with simple drag-and-drop, lyrics and artwork are supported, tracks can be submitted to last.fm, export your library list to HTML, manage notes, repair the iPod and you can even play music directly.
iPodDisk is a Mac OS X application designed to make it easy and intuitive to copy music or video off of your iPod by enabling you to do so within the Finder, or whatever application that can read files. Basically it does so by emulating an iDisk drive and so is accessible like any other volume in the Finder or any other application.
After it starts, iPodDisk automatically opens a Finder window from which you can browse, drag from, or even play music directly on the drive. From a user’s perspective, there’s no difference between the emulated drive and regular local folders, with the exception that the iPodDisk drive is read-only.
gtkpod is a GUI for accessing an iPod via Linux or other unix systems. It allows you to transfer audio and video files onto your iPod and, although it does not support the same advanced media/jukebox capabilities that iTunes has, gtkpod is, in essence, an iTunes for Unix.
It can also import an existing iPod database, including play counts, ratings and on-the-go playlists.
podUp is a Mac OS X application that copies all your music files from your iPod to a folder of your choosing, without having anything to do with iTunes.
It does not attempt to interfere with whatever copyright protection those files may have, it simply copies them, so files bought from the iTunes store will still be authorised only for the computer(s) you have authorisied.
Senuti is a simple Mac OS X utility for transferring tracks from your ipod back to your computer. You can even copy tracks back into iTunes or even add to a playlist. You can even create new playlists and copy these over to iTunes.
In effect, Senuti can be used not only to recover your music or video files and to rebuild your iTunes library, but it'll also recover those precious play counts and ratings as well that aren't stored in ID3 tags.
PS: Bear in mind that simply copying files off of the iPod won't restore playlists and track metadata like ratings, play counts, etc.