If it's just a home use machine, just having /, /home, and swap is probably sufficient. Most applications go in /usr, so it can be handy to have this as a separate partition. /boot should always go on the beginning of the hard drive, and is small (<100 MB) and stores only kernel images/ram disks, i.e. boot related stuff. It's sometimes used to get around limitations with older BIOSes only being able to boot from a kernel located on the first 1024 hard drive cylinders. Usually a lot of mail, WWW site files and such can be stored in /var (but this is all customizable), so usually servers need a separate /var partition.
There's no hard and fast rule on this -- it depends on what the machine is to be used for. For the basic home system, it's probably just sufficient to have a separate /home partition, so you can keep your data if you need reinstall.