WELL, we have a Free games list, a soundtracks list, and hell, even a list on artwork...So, why not one on the best games with mods? I'll start with the ones I know...
Doom trilogy.
Duke Nukem 3D.
Quake series.
Half-Life series.
Max Payne series.
Portal.
The Elder Scrolls III: Morrowind.
The Elder Scrolls IV: Oblivion.
Neverwinter Nights series.
Far Cry.
Star Wars: Empire at War.
Fallout series.
Halo (Technically...it has some mods....)
Star Wars: KOTOR 1 and 2.
Mount and Blade.
Stronghold series.
Unreal Tournament series.
Vampires The Masquerade: Bloodlines.
Trackmania series.
Left 4 Dead.
Left 4 Dead 2.
Crysis.
Operation Flashpoint.
Armed Assault 1 and 2.
GTA series.
Stalker series.
Garry's Mod.
Far Cry 2
Baldur's Gate 1 and 2.
Icewind Dale 1 and 2.
Planescape: Torment.
Warhammer 40k: Dawn of War series.
Hearts of Iron serie (esp. 2 & 3)
Europa Universalis serie (esp. 2 & 3)
Victoria
Europa Universalis : Rome
Battlefield series.
Call of Duty series.
Diablo series.
Deus Ex series.
Homeworld.
Company of Heroes series.
Uplink.
Civilization series.
Freespace series.
Silent Hunter series.
Total War series.
Titan Quest games.
Okay, that's all I know. Add on anyone?
EDIT: hey, why not list some of the best mods for these games as well? Just a thought.

I think it would be more helpful if we listed the best mods, or games that are easiest to mod effectively, depending on the audience you're going for - players or developers.

Left 4 Dead 2 has been on the market for less than a month, and you list it as one of the most moddable games of all time? Through what criteria do you make this claim?
Hm. I echo some of the above criticisms.

Agreed. Crysis should also be on that list if thats the case.

Just the fact that some games have mods doesn't mean they are fantastically moddable. It just means that some fans are technically very proficient. Of that list, I'd say that the UT games and the Source engine games are highly moddable, since they come with free professional modding tools.

This. You have to set it related to quality, or quantity, or customization level, user base, etc. ;)
Halo? Vampires? Portal with just 2,3 tc mods?
I would add Crysis, Operation Flashpoint, Armed Assault 1 and 2, GTA series, Stalker, and maybe Garry's mod on it's own. Far Cry 2 got a map editor too, but not a big thing.

I'd add the Infinity Engine games to that list. Baldur's Gate 1 and 2, Icewind Dale 1 and 2, Planescape: Torment.
Though, like some other games on the list, they would probably only be there because of fans' ingenuity.

Well, I did fuck up the title. Just put any games that have mods for em, so that way we have a list. Adding the ones mentioned.

The Original Dawn of War games. Especially Dark Crusade and the excellent Firestorm over Kronus mod.

Dark Engine games, like System Shock 2, Thief 1 and 2, but just minor, mini mods.
Command & Conquer. There's a lot of RTS games, but not much with high quality mods.

Then that is pretty much every game out there :p (even if it is just as simple as making the generic pixelated female character naked).

Yeah, it might be easier to just list all of the games that have never been modded.

Unreal 2004/III.

That would fall under the Unreal Tournament Series on the list.