Mostly they're a pain to enter on our keyboards.

I used to use .Xcompose which was great, but then I stopped for some reason (like it didn't work right with XFCE or something).

Now I use Vim digraphs. ^K-M.

alt-0151 (numeric keypad) on windows

Some other useful ones to memorise:

0150 the endash, 0133 the ellipsis, 0145 the single quote opening, 0146 the apostrophe/single quote closing, 0147 and 0148 for double quotes, 0149 for a bullet point.