It is not easy to partition a disk in the best possible way. Worse, there is no universally correct way to do it; there are too many factors involved.
The traditional way is to have a (relatively) small root filesystem, which contains /bin, /etc, /dev, /lib, /tmp, and other stuff that is needed to get the system up and running. This way, the root filesystem (in its own partition or on its own disk) is all that is needed to bring up the system. The reasoning is that if the root filesystem is small and is not heavily used, it is less likely to become corrupt when the system crashes, and you will therefore find it easier to fix any problems caused by the crash. Then you create separate partitions or use separate disks for the directory tree below /usr, the users' home directories (often under /home), and the swap space. Separating the home directories (with the users' files) in their own partition makes backups easier, since it is usually not necessary to backup programs (which reside below /usr). In a networked environment it is also possible to share /usr among several machines (e.g., by using NFS), thereby reducing the total disk space required by several tens or hundreds of megabytes times the number of machines.
The problem with having many partitions is that it splits the total amount of free disk space into many small pieces. Nowadays, when disks and (hopefully) operating systems are more reliable, many people prefer to have just one partition that holds all their files. On the other hand, it can be less painful to back up (and restore) a small partition.
For a small hard disk (assuming you don't do kernel development), the best way to go is probably to have just one partition. For large hard disks, it is probably better to have a few large partitions, just in case something does go wrong. (Note that `small' and `large' are used in a relative sense here; your needs for disk space decide what the threshold is.)
If you have several disks, you might wish to have the root filesystem (including /usr) on one, and the users' home directories on another.
It is a good idea to be prepared to experiment a bit with different partitioning schemes (over time, not just while first installing the system). This is a bit of work, since it essentially requires you to install the system from scratch several times, but it is the only way to be sure you do it right.