I will be using a Ubuntu server install as a server for a MySQL database. Is there any benefit to having
/var in a separate partition from the root file system?
I always have
/var on a separate partition and never had problems with it. Doing it this way prevents a misbehaving application (like your database server, but also log files in
/var/log) from eating up all the space on the disk. Of course it also works the other way around. If someone (or some program) decides to write enormous files in
/tmp this would affect your database as well if
/var reside on the same partition.
If you plan on putting parts of your directory hierarchy on different partitions I would suggest to take a look at LVM (the Logical Volume Manager). LVM allows you to dynamically extend your 'partitions' (called Logical Volumes or LVs in LVM parlance). This means that if your LV containing
/var/ is almost full you can extend it, grow the file system on the fly and continue without any interruption to your database.
I've tried to run one of my natty servers with a separate /var a couple of weeks before - it just doesn't start. There seems to be a pretty long history of Ubuntu having various problems with /var on a separate filesystem
So, your best bet is to have some separate data partition, just not put there your entire /var