If you vis the maps, any engine supports transparent water. Other than that, I believe Vr2 and MHQuake are the only engines that support automatic water transparency on non-vised maps.
Many engines support distance fog, including DarkPlaces, Vr2, FTEQW, etc.
As for rotating brushes, I believe DarkPlaces and Vr2 (and probably FTEQW) support them. Other than those, I don't know what engines support them, but I'm fairly sure there are others.
Copying player attributes from server to server isn't really an engine feature, in my mind. That would be something the game coder would have to rig up himself, I think. I could be wrong though.
Vr2 supports Q1BSP map sizes a bit larger than most Quake engines, and HLBSP. DarkPlaces supports large Q1BSP map sizes as well as HLBSP and Q3BSP. FTEQW supports HLBSP, Q2BSP and Q3BSP.
Links to the engines mentioned above:
http://entar.quakedev.com
http://icculus.org/twilight/darkplaces
MHQuake doesn't have an active website afaik, but if you look around or ask mh on the QSG forums, you can probably get your hands on it.
http://fteqw.com