How to change the color of the tilde characters indicating the filler lines after the last line of a buffer in Vim?

Try this:

:highlight NonText ctermfg=12

12 is the default color; change as you see fit.

In Vim 8, you can set the EndOfBuffer highlight group separately from NonText:

highlight EndOfBuffer ctermfg=bg

Lucas is right but if you want to change the colour in gvim as well I think you need guifg= as well as ctermfg=

i.e. :highlight NonText ctermfg=*color* guifg=*color*