The Voyager OS (old school) is as close as the modern incarnation of Moog ever got to the original Model D - but it can't save presets, and it's been discontinued anyway, although they do show up on eBay all the time.
The Voyager and Voyager RME (rackmount brain only) are probably what you want - they have three oscillators (like the Model D) and were intended as a modern version of the D. They are still in production and there are tons of used ones all over the place. You can save presets and the touchplate is an awesome feature. They are incredibly well-built and are awesome instruments. I've had one ever since they first came out and it still plays as if it were brand-new, 14 or so years later.
The Slim Phatty has been discontinued, and falls short of the D in terms of architecture.
The new Sub Phatty might be a good choice - it's still missing that third oscillator but it has a couple of nifty new features and can save presets, and it doesn't cost an arm and a leg. I quite like this little guy.
The Studio Electronics pieces are quite nice as well, and those guys really know what's up with a Model D as they used to strip 'em down and rackmount them and later they built their own 1:1 clone in a rack - and the SE-1 is a great synth as well that will not disappoint.
But... the original Model D just has.... something... that the new Moogs and the SE synths don't have. There's a characteristic "thump" to every note that adds an almost kick-drum-like bit of boooof to every note that seems to be missing from all of the modern incarnations. I was talking with Sean Beavan (ex-nin engineer) about this one time, and he mentioned that Jeff Turzo (from God Lives Underwater) who is now building studio outboard gear under the Overstayer brand (good stuff BTW) had discovered when analyzing the Model D circuitry that there was a design flaw (or maybe intentional feature?) that caused this "thump" in the Model D's output amps or something, and Jeff has included this design flaw/feature in one of the Overstayer pieces. I can't remember which piece it was that had this feature (I think it was one of the compressors he makes), but it was specifically intended to try to bring some of that Model D thumpy magic to a piece of outboard. Sean described the thumpy circuit as being part of the Model D's VCA stage, so it makes sense that it would be one of Jeff's compressors that had this included.
So... yeah. The original Model D is ancient, expensive, and might need work if you buy a shaggy one - but it is the only thing that has that... thing. The difference between the D and the modern Moogs can be subtle on some sounds, but is quite noticeable on bass sounds in particular. The good news is that there are lots of them for sale at any moment and everybody knows how to fix them, so out of all the vintage synths you could lust after it's probably one of the safest buys out there.