As Ethan Schoonover pointed out in his vim colorscheme readme, to make the colorscheme work first you have to configure your terminal colour palette.
In terminator there is a github repo that holds the colour configuration for the dark and light scheme.
The problem is that that palette isn't right either :P, the correct one is the one a guy posted in an issue on that same repo.
The correct configuration is the following (at least for the dark scheme):
[[solarized-dark]]
palette = "#073642:#dc322f:#859900:#b58900:#268bd2:#d33682:#2aa198:#eee8d5:#002b36:#cb4b16:#586e75:#657b83:#839496:#6c71c4:#93a1a1:#fdf6e3"
cursor_color = "#eee8d5"
foreground_color = "#eee8d5"
background_color = "#002b36"
After that, you have to configure the solarized colorscheme:
syntax on
set t_Co=16
set background=dark
colorscheme solarized
A couple of things to have in mind:
Normally, the set t_Co=16
line is not necessary because most terminal emulators only support 16 colours (terminator for example). But I rather be explicit than implicit (specially if you are going to sync your files between multiple computers).
The line set g:solarized_termcolors=16
is the default, so you can put it or not: it won't make any difference.
In my experience the 256 colour version is better (I like more grey background over a blue one; but that's personal taste :P). Contrary to what everyone could think, the 256 colour scheme is actually the 'fallback' being the 16 one the default. Yeah, weird, most people would think that 256 > 16. Anyway, to use the 'fallback' you have to change the lines to the following:
set t_Co=256
set g:solarized_termcolors=256
There are actually some issues with colour output in other CLI applications, I suggest you to go and read Seebi article about dircolors and an ongoing(?) discussion on the solarized github issue tracker.