Much as we love the Duke Nukem 3D High Resolution Pack, this Unreal Engine 3 remake-in-progress from "amateur" developer "fresch" puts it to shame.
fresch asked permission from 3D Realms' Scott Miller and George Broussard to continue with his project after discovering Gearbox Software had obtained the rights. Miller responded, saying it "might be doable" (turns out 3DR is still in charge of the old works) and asked for screenshots (see above and below -- he stresses they are early, so "have mercy"). Currently it's up in the air, but if it does progress, we'll be sure to update you.
fresch notes he'd need a team if it's greenlighted. The plan from there would be to release a one map multiplayer game to get things started and a final release some years down the line.
The developer has also worked on remakes of Daikatana and SiN -- both of which were canned for different reasons. You can check them and also some high res shots of Duke Nukem NextGen (as it called) via the source.