Turning on HDR change how light is rendered. Look at the attached screenshot to see how.
To turn on:
Press the title key (the one next to the 1 button ) while in the game and write "\r_hdrrendering 7" (enter) and then "\r_fsaa 0".
Combine that with the rendering modus "cold" in the setting produce nice results IMO. You lose FSAA but the overused hdr gives FarCry more charm.
Ps. "\e_vegetation_sprites_distance_ratio 100.000000" might be a good idea too.

Hmm, that does look rather nice. Know of a permanent setting so you don't have to set it each time?

It was permanent when I did it but you can always make a shortcut, ie: "C:\Program Files\FarCry\Bin32\FarCry.exe" "r_hdrrendering 7" "e_vegetation_sprites_distance_ratio 100.000000" "r_fsaa 0" (with the quotes)
Edit: To undo the settings write "r_hdrrendering 0" and "r_fsaa 1" (the later only if you want AA).
e_vegetation_sprites_distance_ratio adjusts when vegetation is reduced in quality (I assume turned into flat sprites). Might impact slow computers but for modern hardware it shouldn't matter.

If you want those settings to be persistent, you can either edit the shortcut as you mentioned above, or add the settings to a file called Systemcfgoverride.cfg in your Far Cry directory. This should be the same directory that the Bin32 folder is in.
I don't have the GoG version yet so I can't tell you the exact folder layout.

If you use an newer graphics card, you should be able to have both HDR rendering and anti-aliasing at the same time. At least, it works here on my 4870 X2.
I find the setting too high, though. I would recommend not setting it higher than "r_hdrrendering 2". It probably depends on which card you use, might be worth experimenting with other values, such as these:
r_HDRBrightOffset = "6.000000"
r_HDRBrightThreshold = "3.000000"
r_HDRLevel = "0.600000"
You can find all these settings in system.cfg in your Far Cry root directory, along with a lot of other options as well. You might want to have a look at Tweakguides' excellent guide here for more tweaks and fixes: http://www.tweakguides.com/Farcry_1.html
Late edit:
I have found that these settings are optimal for my system, and gives rather eye-popping visuals for their time:
r_HDRBrightOffset = "6.000000"
r_HDRBrightThreshold = "3.000000"
r_HDRLevel = "0.500000"
r_HDRRendering = "1"
Use this together with "r_RenderMode = "2"" for the best effect. The HDR rendering should now be subtle, used just right to improve the atmosphere, without overly saturating the visuals. Enjoy!

I wish you'd written this few weeks earlier when I was playing the game :). I tried changing r_hdrrendering, but the effects were terrible.