The singleplayer is good fun, whether its blasting monsters, Duke spouting one liners, or the high interactivity of the world. At the time, Duke's only real competitor is Quake. The only thing Quake had going over Duke was that it was fully 3d, yet Duke's world was so vibrant and interactive that Quake couldn't hold a candle to Duke. There were a total of four episodes (a fourth being added via the Atomic Edition or Plutonium Pack expansion), each of which took Duke to various locations, from a Red Light distrcit to a space station. There were tons of contemporary references thrown in as well, everything from a "Doomed space marine" to a secret area of Captain Picard's Enterprise from Star Trek.
The weapons were also inventive and are, to this day, some of the most fun weapons in any FPS game. You of course have your classic shotguns, rocket launchers (RPG), pistols and machine guns, but there were also some more unique weapons such as the freeze gun, which would freeze enemies that you could then shatter with a kick, the shrink ray, which would shrink enemies that you could then stomp on, and the expander, which would make enemies expand until they blew up (added by the Atomic Edition).
The maps, as mentioned were definitely creative and to this day are some of the most memorable maps of any FPS. Duke supported singleplayer, co-op, and deathmatch, and the maps were all designed well enough that most maps fit perfectly for each gameplay type. There were also rudimentary bots included with the game, however the code for bots at the time was so new that they pretty much sucked.
Another plus to Duke is the build editor that shipped with the game, to my knowledge Duke is one of the first games that, out of the box, shipped with some sort of content creator. It wasn't that hard to use either. There is a wealth of addons available for Duke, from commercial addons Duke it out in DC (GOG, PLEASE get this up on the site!) to non-commercial (free!) addons and tons of user created maps.
Finally, in recent years, 3d Realms/Apogee have seen fit to release the source code for the build engine, the engine that powers Duke Nukem 3d. What does this mean? It means that you can now download a custom created engine designed to work with XP/Vista, adding more modern graphical bells and tweaks, such as 3d models to replace the classic in game sprites and high res music, updating Duke for a new generation.
Duke is an FPS that will forever hold a place in my heart. Sure, some of the jokes may seem a little dated (the game DID come out in 1996 folks!) but when it comes to FPS games, it really doesn't get much more nostalgic than Duke (Doom and Wolf were fun, but Duke had a level of interaction with the world that neither of those games ever had).