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 /tmp and /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.