Nikon might not care, but you do
For the purposes of this article, I'm going to assume you're not a buy-a-kit-and-forget-it type of shooter. I'm going to assume that you're trying to put together a reasonable lens kit for your DX body and coming up short with Nikon's meager offerings. But different types of users have different needs, so there's not just one possible set of lenses you might want to obtain. So I'll break things down by various different users.
Right up front we have a class of DX users that need a bit of extra love: those that buy into lower end Nikon DSLR bodies. These bodies lack screw-drive motors for focus and must be used with AF-S (Nikon) or HSM (Sigma) lenses (Tokina and Tamron also have a few lenses with built-in motors, but no formal name for that). These cameras also don't have working exposure meters with most older manual focus lenses. The cameras I'm talking about are the D40, D40x, D60, D3000, D3100, D3200, D5000, and D5100. If you have one of these cameras, you're even more crippled in putting together
a functional lens set than others. You've got Nikon's 17 DX lenses, Nikon's AF-S FX lenses, plus perhaps a dozen lenses from the third parties to choose from. That's it.
Until the D3200 came along, the low-end kit lenses were perfectly acceptable on these bodies. Thus, the 18-55mm VR and 55-200mm VR made a perfectly viable starting point, and often were as much lens as most of these users ever cared for. Even the 18-200mm (to replace both kit lenses) was a viable solution, though a bit of a large lens on the smaller DX bodies.
The shame is that the D3200 is a very good camera in tems of its image quality capability. It needs better. It deserves better. And it starts to show how limited the Nikon DX lens choices really are. First, we have the diffraction thang. Having a best case of f/4 or f/5.6 through most of your shooting range really puts you in a bind: we hit diffraction limited apertures at about f/8 for a full sized print viewed at 50cm. These variable aperture lenses aren't close to best wide open, so we're immediately starting into a level of compromise when we use the slow zooms on the D3200.
I would strongly encourage a different approach for the savvy D3200 user: the Voigtlander 20mm f/3.5 (manual focus), the Nikkor 35mm f/1.8G, and the Nikkor 50mm f/1.8G. Supplement any telephoto need with the appropriate FX lenses. If you really need zooms, see my comments further down for other bodies; the 16-85mm works well on the D3200, too.
The Underwater User
If you're going to go down under (the surface, that is, as in diving) and want a good general purpose lens, there's probably only one lens you really want to consider: the Tokina 10-17mm f/3.5-4.5. It's not the greatest of above water lenses, but it's nearly perfect for large fish and mammals (including your fellow divers) underwater. If you're more into photographing the small life in the coral, then you need a macro. Your macro choice will depend a bit upon what you like to photograph, but the water's impact on focal length means that you can generally use a bit shorter Micro-Nikkor than you would up on land. The 60mm, 85mm, and 105mm are all logical candidates for different subjects. The 85mm, being a little slower, is probably not the choice unless you're using flash.
Reach, reach, reach. The typical approach is to try the Sigma 50-500mm or the Sigma 150-500mm. These are the cheapest ways to get to 500mm (750mm equivalent). But I don't think they're strong enough at 500mm. The 150-500mm was good out to about 400mm, but if you're only going to 400mm, there are other choices that start to come into play.
Short of buying one of the FX exotics (typically 200-400mm f/4 or 500mm f/4), there's no great answer for the DX user seeking maximum reach with maximum quality. I actually think that some people might be better off with the 70-300mm f/4-5.6 VR on a Nikon V1 with FT1 adapter (810mm equivalent), especially if we're comparing D300 (12mp) versus V1 (10mp). It's not a perfect solution, as you lose continuous autofocus, but you also gain 60 fps (with focus distance fixed to first shot).
What happens is that a lot of folk end up in the "compromise position": the 300mm f/4 AF-S (non-VR) or the 80-400mm f/4-5.6 VR (non AF-S!). The 300mm works decently with the TC-14E, which gives you 420mm f/5.6, but it's not VR, which makes it not a great handholding choice. Another possible solution is the Sigma 120-300mm f/2.8 OS, but I think it's just a little weak with the 1.4x teleconverter that'll get you to 420mm f/4. But if you're thinking about wandering around birding with a long lens, I'll be that most DX owners that don't spring for the expensive exotics but want quality are using one of these three solutions (300mm +TC, 80-400mm, or 120-300mm).
The Two Lens Solution
If you never go particularly wide (i.e. don't need wider than 24mm equivalent), and don't need DOF isolation or low light capability (i.e. f/2.8 or faster), there is a two lens solution for DX shooters that's high quality:
That covers 24mm to 450mm equivalent, and does it remarkably well. I call this the "amateur solution," as it basically gives them all the focal lengths they need and these users aren't as prone to worrying about DOF isolation issues. Watch out for diffraction impacts on the D5100, D7000, and D3200 bodies, though. Try to stay at or under f/11 for the first two, f/8 for the latter.
The I Just Want a Complete DX Systemer
What's so hard about a trio of zooms, a trio of primes that cover the basics well? Answer: Nikon only gives you two of the six.
This type of shooter has decided that DX is their system, and just wants something close to equivalence to what they could get with other systems. A good wide angle zoom. A fast stabilized mid-range and telephoto zoom. Three small primes. Maybe a convenience lens (but they tend to get that when they buy the camera as a kit).
Let's take each of the six lenses individually.
Wide zoom: Nikon offers two, and both are very good (10-24mm and 12-24mm). Sigma offers some similar options. If you need fast apertures for this lens, then you're stuck with Tokina's 11-16mm f/2.8. Plenty of options here, and for most people Nikon's 10-24mm is perfectly fine. The rest will tend towards Tokina's 11-16mm f/2.8. If you're a tightwad, you look at the Sigma and Tamron offerings.
Mid-range fast zoom. Nikon really only offers the large and unstabilized 17-55mm f/2.8. A very good lens, but the lack of stabilization tends to send folks elsewhere. In my opinion, the only better option that's stabilized is the Sigma 17-50mm f/2.8 OS. It's smaller and lighter than the 17-55mm, and if you get a good sample, may even be optically sharper.
Telephoto fast zoom. We used to have two options here, but now only have the 50-150mm f/2.8 OS from Sigma. That lens is starting to get large enough that you have to consider whether to just get the Nikkor 70-200mm f/2.8 VR, though if you're always going to stay DX, you probably get the Sigma. I haven't tested the OS version of this lens yet; the non-OS version was good, though slightly weaker at 150mm.
Wide prime: Bueller? No one sitting in this chair. I suspect that Nikon thinks the old 20mm and 24mm f/2.8 D lenses suffice here. They're certainly small enough to fit a DX prime kit. The problem is that they're not modern designs and thus aren't exactly stellar lenses on the DSLRs. The 30mm and 36mm equivalent focal lengths aren't particularly wide, either. If you need "really wide" consider the 10.5mm f/2.8 and de-fish it in software (I've also had decent results with the 15mm Sigma de-fished). Otherwise your best bet is one of the 20mm choices, with the Voigtlander 20mm f/3.5 (manual focus) still being my favorite.
Normal prime: The Nikkor 35mm f/1.8G is a gem. Modest in price and good in quality.
Telephoto prime: Nikon doesn't have a DX telephoto prime (other than the 85mm f/3.5 Micro-Nikkor, which typically isn't the lens people are looking for here). Something really fast that's suitable for portraiture. That means a focal length of 50-70mm. Well, the 50mm f/1.4G and f/1.8G do play okay here if you can deal with a weak telephoto effect and the perspective it generates. The f/1.8G is like the 35mm: modest in price and good in quality. Consider it strongly, even though it isn't a DX lens. At the far extreme, the 85mm f/1.8G would also work decently in a "DX" prime set. But I'm going to suggest a completely different lens: the Tamron 60mm f/2 macro. While you wouldn't ordinarily think of it as the telephoto prime choice, it's the perfect focal length (90mm equivalent) for portraits, and fast and sharp enough to work just fine for that.
The FX Way
Here's where things start to get problematic. Almost certainly, Nikon's DX strategy has been tailored to this: buy FX lenses.
The problem, of course, is that FX lenses are bigger, heavier, and more expensive than the DX lenses you could have had. So Nikon is not only extracting a penalty tax from you if you go this route, but also then prepares you for buying a more expensive FX body some day. Disingenuous at best. But here we go:
|DX Needs This Lens
||Buy This FX Lens
|24-70mm VR equivalent
||16-35mm; you come up a bit short at the long end, but that's not the problem end for DX.
|70-200mm VR equivalent
||70-200mm; you are a bit long and you have a gap you now need to fill between the 16-35mm and your 70-200mm, but a 50mm f/1.8G works just fine for that.
|20mm prime equivalent
||14mm f/2.8. Biggest damned 20mm equivalent for any system extant, but Nikon doesn't care. Not a great lens, but if you don't mind correcting the chromatic aberration, usable as a 20mm on DX.
|28mm prime equivalent
||20mm f/2.8. Hey, at last a smaller lens. But not an exceptionally great one, even on DX. I like the Voigtlander 20mm f/3.5 (manual focus) better.
|35mm prime equivalent
||24mm f/1.4G. Yeah, that's another hand full, and expensive.
The rest of what DX needs are either close to available via DX/FX lenses (50mm, 85mm prime equivalents) or completely missing in action in both DX and FX (something like a 70-300mm equivalent in DX, for instance, and FX really requires a 100-400mm VR to exist).
The Canon Way
As many Nikoneers discovered over the years, it's easy enough to adapt a Nikon F-mount lens to the Canon mount. Indeed, many Canon 5D shooters used to use Nikon wide-angle lenses on their cameras to get the best of all worlds (inexpensive FX, quality wide angle). But a few wildlife photographers have discovered the opposite: buy a Canon 7D and 100-400mm f/4.5-5.6 or 400mm f/5.6 to handle the long reach needs. Of course, you're still stuck with a Nikon DX body's weak wide angle and mid-range side for your other work, so maybe you might want to think about doing that with, oh, say an m4/3 camera? ;~)
The Full List
Okay, B&H lists 69 lenses for DX. Let's look at them another way. Here's my current take on the lot:
Nikkor 16-85mm f/3.5-5.6 VR AF-S
Nikkor 35mm f/1.8G AF-S
Nikkor 10-24mm f/3.5-4.5G AF-S
Nikkor 10.5mm f/2.8 fisheye
Tokina 11-16mm f/2.8 DX-II
Nikon 12-24mm f/4G AF-S
Sigma 17-50mm f/2.8 OS HSM
Nikkor 17-55mm f/2.8G AF-S
Nikkor 18-105mm f/3.5-5.6G VR AF-S
Sigma 50-150mm f/2.8 OS HSM
Nikkor 55-200mm f4/-5.6G VR AF-S
Nikkor 55-300mm f/4.5-5.6G VR
Tamron 60mm f/2 Macro
Nikkor 85mm f/3.5 VR Micro-Nikkor AF-S
Tokina 10-17mm f/3.5-4.5 fisheye (for underwater use)
Yes, you read that right. 69 lenses, only 15 of them recommended. Or put another way: 17 Nikkor DX lenses, only 10 of them recommended.
The simple truth of the matter is that DX users have been filling out their lens kit with FX lenses, mostly because they're forced to. In some ways this is distorting everything. DX users are putting larger-than-necessary lenses on their cameras, they're paying more for lenses than they probably should be, and they're discouraging Nikon (and others) from making DX-specific lenses by dipping into the FX offerings.