I know it is something people are rather lax about now, but there may be some good sense, long-term, in placing certain things on different partitions. The purpose is to exercise some control over space use; even on a laptop there will be programs that keep filling up the disk until you run out of space and have find where the problem is - that is a lot easier if you don't keep everything in a single filesystem. Also, you don't want to find yourself in a situation where almost everything is impossible because there is no space left on the disk.
Another thing that can be helpful, certainly on a server, is to use either logical volumes (see: lvm) or a filesystem like zfs. This is much more flexible than partitions - not only can you change the size of a logical volume without hassle, but you can add more harddisks to your volume groups when you need more space.
Also, you don't need to have partitions at all, if you use volume groups or just have one filesystem on a disk, just use mkfs directly on the device.
I usually put the directories that tend to grow a lot, in separate filesystems, certainly /tmp and /var (most logs end up in /var/log and can become very large), but also split off /var/lib/mysql from /var if you use mysql.
