Is there any advantage(s) to setting up separate partitions in any order for /, /root, /bin, /sbin, /sys, /usr, /opt, /ad nauseum on Slackware?

Not particularly. It is advisable to have a separate /home partition and - perhaps - a separate /boot partition. Anything else would be overkill.

If you use Hard Drive Disk, need given speed in start and end of disk.
In start:
Latency is low
Throughput is low
in end of disk:
Latency is high
Throughput is high

So, recomend:
/
/var
/tmp
/usr
/home

The only thing I would recommend is to use a ramdisk for /tmp if you have an SSD... Other than that, it's kind of your choice and depends on what you want to do with the OS.. A strictly web-server (even with a mail server) would benefit more from a different partition for /var and have almost no use for a /home partition, whilst a strictly desktop/laptop system without web/database use would benefit from a /home partition and have almost no use for a /var partition...

As for /usr.. It's best to leave that in root.. That's an old recommendation which quite frankly doesn't mean much this days (and might even get you in trouble on some systems)....

Yes there is, although I wouldn't advise you to set up /bin and /sbin and /ad nauseum [sic] as separate partitions. If you put your mind to it you might even be able to work out for yourself what those advantages are: retention of data in /home if you ever have to reinstall; retention of local and optional software in /usr/local and /opt if you ever have to reinstall; reduced disk seeks and write times, which as you might know reduces wear and tear on mechanical drives; prevention of an overflowing /tmp hosing your system; ability to use a non-journal filesystem on mounts where journals are not needed; migration of /var/log to separate disk; and so on, ad nauseam.

Multiple distributions can share the /tmp partition if you multi-boot. Clear it in /etc/rc.local. (Swap can also be shared of course.) Also /tmp and /boot can be ext2. Many partitions can have nosuid and nodev. noexec doesn't work very well -- there is always something that must be executed.

Having /usr, /tmp, /var and /home separate prevents / from becoming full.

/home is separate for me but it only contains a few configuration files. I have /data instead so all distributions can use it, and it's ext3 for BSD.

Hey Nix84, as you can see from the answers above, the answer to this question is: "It depends."

What are your goals with this machine? Is it going to be a server or a simple desktop? If it's going to be a desktop machine, would you like the option of installing 3 different Linux distributions on it?

Without knowing more about your circumstances and goals, it is not easy for someone to prescribe the optimum solution for you.

If you're not 100% sure, you can always change things later on. It is not hard to move an existing Slackware installation to a different partition or set of partitions.

Without knowing what you use your system for and what you are seeking to optimise, I can only say that I have not found separating a system out into many partitions to have a significant impact for me. My Slackware desktop machine for a few years had separate partitions. I used it for heavy multimedia work (video editing, 3d compositing, and music composition) and could never tell any difference between it and my laptop, which ran Slack on a single partition/drive (obviously the GPU was different, but I am talking about system performance).

There may be exceptional cases that do see a benefit, so I am only telling you my experience.

One thing I do like is to have /home separate, but that's only because it is convenient (although not essential) when upgrading.

As long as you have backups and good utility/install disks, do what you want. For me:

/boot: keeps kernels, maybe a minimal rescue system, allows LILO to work with otherwise-unsupported file systems.
256 MB - 384 MB gives a persistent option of whether a tiny rescue system goes here. Always formatted something old like JFS, ext2 on rare occasion.

/: keeps system

/tmp: only if I abuse /tmp or want encrypted /tmp

[swap]: swap partition

/home: LUKS/cryptsetup if I care about the data, still separate if I don't care.

/mnt/emergency: a non-X11 alternate system, in case I get into trouble; added to LILO boot menu

/mnt/backup: something on the drive to hold backups that I'm too lazy to store off-disk

If you're adventurous, you could use fio (a separate download) to benchmark the disk to see what goes where. Should you get the test file right, fio can generate nice gnuplot plots, and gfio can graph it all in real time.

I tend to put the alternate system and backups on slow parts of the disk. swap goes later because I rarely use it, though some tend to put it on a faster part of the disk.

At any rate, to have separate partitions makes backup and restore a bit easier for me, especially if I'm using xfsdump. Also, I'm usually way off the beaten path when it comes to kernels and kernel config, and that might get me bitten here and there.