Unreal 2004 and III doesn't exist. :)
There's unreal, unreal:rtnp, unreal 2, ut1999, ut2k3, ut2k4, ut3.
EDIT: add Battlefield series, Call of Duty series, Diablo series, Deus Ex, Homeworld.

If there hasa been mentioned Dawn of War, then Company of Heroes are good moddable as well. (I'm looking at the Battle of the Bulge mod and others)

Don't forget Uplink...although most of the mods have been mostly skin mods and the like, I do remember reading about an FBI mod for Uplink.

That's a pretty pathetic trolling attempt. ANYONE who plays video games would know what "Unreal 2004 and III" means.

Trolling?! where? Man, don't be radical just because of a tiny post on a forum.
In my opinion, UT series count for all of them. But if Rohan15 wants to specify it, so was just a suggestion not-so-well-suggested because I use my time for other things than writing this, ok?
What I meant was: UT series (unreal, unreal:rtnp, unreal 2, ut1999, ut2k3, ut2k4, ut3).

All Paradox Interactive games :
Hearts of Iron serie (esp. 2 & 3)
Europa Universalis serie (esp. 2 & 3)
Victoria
Europa Universalis : Rome
...
I know, those are not mainstream games.
The Civilization serie is extraordinarely modable.
Freespace 2 (SCP) generated a lot of mods, too.

Yea, I was going to say Freespace 2 as the mother of all moddable games.

The Silent hunter series (including destroyer command, which uses the SH2 engine).

Total War games (especially from Rome on) also enjoy a good modding community.
And Titan Quest (+expansion) is also a good candidate.