Many partition their drives for organizational reasons. For instance you can create a partition for /home for all of your users to keep all user data on.
Partitioning is also a good way to ensure that a filling a file system won't kill your server. For example, if you have a / partition in Linux that fills up your drive and a user's script fills up that volume your whole server could go down. If you create a /home partition or /var and /tmp partitions then a user filling up /home won't take the server down. It may cause problems with your other user's data, but it won't cause the whole server to go down, so you can still log in and fix it without having to contact us for reboots and whatnot.
What size and type partitions you use depends on what you plan on doing with your server. If you can elaborate on that we can recommend a good partition size for you.
Hope this helps.