I am assuming you are talking about running this hard drive under a Windows OS, if that is the case then @KCotreau is right, there are no performance benefits. If you were to run it under a *nix OS then there might be more of a selection as far as what kind of filetype would work best on what filesystem, or possibly the difference between LVM and native partitions.
I personally have my network drives setup as all different locations, a "Music" drive, a "Videos" drive, etc... I find this helps me keep more organized as I am forced to pick a drive that fits the type instead of just dropping it in the root of the drive and forgetting about it.
There are small benefits you can gain besides performance based ones if you partition the drive. For example, you could encrypt your "Documents" drive, yet leave the music and video partitions open. Also NTFS allows drive compression to save disk space, but this can degrade performance, so maybe you dont want your "Videos" compressed because then they wont stream as well, but perhaps compressing the "Music" partition is fine because you only really listen to music on your mp3 player. All of these features can be done on the folder level too, but doing them at the drive level really helps enforce that it is always so.
If you DO partition your drive I would suggest creating whats called and "extended partion" across the whole drive. The reason for this is that you can only put 4 primary (native) partitions on one drive, whereas if you create an "extended partition" first, you can make as many "logical" partitions as you want after that!
One last thing, if you DO partition it all up, just be aware that if you end up filling one partition completely full (lets say the videos partition), you could have a heck of a time resizing the other partitions to make room for more space on video partition. It is also dangerous too. I have had partition resize and moves fail on me half way through. This left all of my data in a partition that was neither declared, or in the right place(es)... which makes recovering everything that much more complicated and more unlikely. So ALWAYS backup your data to somewhere else before messing around with partitions that have data on them.