You can’t have any of them. For example, in TeX, the back tick gives a single left quote and two of them give a double left quote. Let’s see if it works in markdown. No, it doesn’t. There isn’t a single symbol on the keyboard that isn’t used in TeX. What I have is a program whereby I hit the right alternate key and then the right combination to get characters I want. For example, I get ¢ by using the combo rt.alt-|-c. Or è by rt.alt-`-e. The program is called Win-Compose. Of course you are limited to the extended ASCII characters (the ones numbered 128-255).
The silcrow. §.
It’s on Finnish keyboards, and, obviously, I can type it using a compose key, with some effort at remembering the keystrokes, but it’s needed.
And the pilcrow. ¶.
The usual diacritics are fine as is. ẞ is easy enough, as is é, or è, or ñ, or ç, or whatever.
As a foe of USC, I use it a lot… u$¢
Click here, click Copy. On the keyboard would be better.
Or Alt-0176 (on the numeric keypad).
I keep the six or so codes I use most often on a Post-It™ note:
™
¢
°
²
½
× (that’s multiply, not x)
As a unixhead and vi aficionado, I second this.
I think I don’t have a use for square brackets, but everything else gets used a lot
Swiss keyboard has it as well. And if I use shift, with the same key, I get a degree symbol °. Hadn’t even noticed, as that key is to the right of the number 1 key.
That said, I know several programmers who prefer an American keyboard layout for the special keys.
My candidate would be the AltGr key, so then I could have a lot more symbols on the American keyboard.
Square brackets are essential to me for some legal citations, and for editing Wikipedia.
You fellows are aware that most keyboards have a bunch of potentially useful modifier keys, like Alt, Alt Graph, Compose, Meta, Shift, Fn [whatever they happen to be called], and so on? 
There should even be some special combination to switch to alternate keyboard layouts, in case one is not enough…
PS many keyboards come with three (maybe more? who knows?) characters painted on many of the keycaps; e.g. 4$€
And for nested parentheticals (which I don’t use that often [but often enough]).
Alt Graph? Compose? Meta? What the heck keyboards are you using?
For what to bump off, I still say that the single greatest innovation on Chromebooks is getting rid of the caps lock key. Scroll Lock and Pause/Break are useless, but they never hurt anything. But Caps Lock never does anything but cause trouble.
This. The first thing I do on any new computer is set a shortcut key for it.
I use Pause/Break all the time. Or at least I used to, until I got a keyboard without them, and had to remap it to a different combo. Still annoyed at that, but I like the keyboard in too many other ways to give it up.
I concur. Bumps off the ^.
A humble Sun type 5c keyboard has Caps Lock, Alt, Meta (x 2), Alt, Alt Gr, and Compose all on the bottom row
A Gigabyte gaming keyboard has Control, “Window” (not sure if that counts as Super or Meta or whatever, but it’s there), Alt, Alt Gr, Fn, Menu, and Control [again, I am talking about the row including the space bar]
A more compact Gigabyte has Control, Window, Alt (x2), Win Lock [not a modifier], Fn, and Control
Are keyboards with loads of extra modifier keys somehow rare?
Definitely the apostrophe with the period under it. I did it time and time again with the old World War II era Royal manual typewriter that I had growing up; it had belonged to my grandfather (and weighed about 65 pounds).
Do Microsoft’s stupid custom keys count as “keys”? I use the “Windows” key maybe once a year, and the context menu key precisely never. In fact my current keyboard doesn’t even have the menu key (it’s replaced by a lighting control key). So I’d get rid of the Windows key and replace it with a key that had the degree symbol º in the lower case position and é in the upper case. The latter not because I write anything much in French but because English occasionally incorporates French words that need that “é” character. Of course you might also need è, ê, or ç. Those are more rare. Deal with it!
IMHO there’s no need for the em dash because two consecutive dashes traditionally serve the purpose in typewriting, and in typography the software is generally smart enough to convert two consecutive dashes to an em dash – even Discourse does it for you.
Nonsense.
But, if required, it’s simple enough to reassign the caps lock or search key to whatever purpose required.
I’d just use it as a dead key/compose key and try really hard to not be some nerd who uses the numeric keypad for anything other than entering numbers.
One cannot type in any language which uses diacritics or non-Latin characters using some l33t alt-codes.
Assuming one is able or willing to communicate in any language other than po-dunk “thar ya go” hillbilly British.
It seems to be mapped to the “Super” modifier in Linux; I have it set up with some useful shortcuts (including, but not limited to, switching to a different window or desktop 