okos , let me see if I can provide a little insight. This is not definitive, just from my recollection ( and at my age .... )

What is the importance of so many partitions?
Depends on the OS, the equipment, environment, needs, and desires.
Would it not waste space if nothing is added to certain partitions?
of course.

There were ( and still are ) reasons for partitioning drives.

OS: This one speaks for itself; different operating systems place things in different places. It may not just be the difference between unix and linux ( although they are similar ) but between flavors, and even versions of each. ( I know, you will point me to FHS ( otherwise known as FSSTND). ) But play around with them and you will see the differences.

Equipment: this one is important. Is it older or newer equipment? Is it x86 or sparc? ( I am not even a novice on sparc equipment, but I understand there at least were some quirks concerning partitioning schemes and requirements not found to those used to x86. )

As for age? Older x86 equipment, because of BIOS restrictions, required that the boot loader be in the first 1023 cylinders of the hard drive. The /boot partition is normally under /, so if you used the entire drive for the /, the system would put /boot first and you would have no problem ..... until you started changing, modifying or adding kernels. Then portions could be overwritten, placed elsewhere, etc. Now the system BIOS may not find all the files needed to boot! Thus people started creating a separate /boot partition in the first 1023 cylinders so the BIOS always had access to it.

These restrictions do not exist today. Most modern BIOS do not suffer from those old restrictions, so the /boot directory can be almost anywhere on the disk. Many linux distros will run happily with a single / partition and no others ( yes, not even swap, depending on the memory available, kernel size, etc. )

Environment: Is this a critical server? Is it a workstation environment? Home?
Again, for a simple home setup, all you really need is one partition. For a critical server, you probably have to have separate /boot , /, tmp, /var and home, and yes swap partitions. A machine in between? Maybe, in-between?

A /var partition in a more critical machine is important because that is where log files, print spool files, etc. are stored, and should they get out of hand you don't want them writing over other data. Most of the others I believe have already been mentioned, but in the days of the 2.0 kernel, Red Hat even recommended separate partitions for /usr/local ( where they said software not installed using RPMs should be kept ) and [i]/usr/src ( where you build your kernels. )

As for how big the /boot partition should be? On a 2.0 linux kernel it was quite happy with a 5-10 MB partition ( this was considered generous. )
Today, a 1 GB is more then sufficient, but considered the norm. ( the Fedora boxes around me right now are using less then 18MB of their /boot partitions, and each have two versions of the 2.6 kernel in them. The SUSE box is using less then 7 MB ( only one kernel. ) With the size of today's drives a little space wasted here can save yourself some grief in the long run, especially if you update kernels regularly and keep all the old ones. If you are constrained to a smaller hard drive or portion thereof, cut that in half: you should still have plenty of room, just watch those kernels don't build up!

As for the size of the other partitions? I suggest an installation to test the waters, load it up with all the software you will be using, then check usage. ( use something like Baobab that is available with Gnome. ) Then you can re-install, correct mistakes, and have it custom tuned the way you want.
But I still like to have at least separate /boot, /, and swap partitions.

Or, just use the defaults that come with the OS. That will usually work!