I'm wondering if anyone has an opinion about Nikkor vs. Tamron and/or Sigma lenses. Is it worth the extra money to purchase Nikkor lenses? I haven't had the chance to compare these. Are the Nikkor lenses sharper? If you think Tamron and/or Sigma are comparable, is there a certain brand that is superior?
There are enough variations in lenses that it's hard to make a generalization about an entire brand vs. another. A lot of folks stick to the lenses from their camera manufacturer and I think that in the past the quality tended to be better. That said, some of the third party lens manufacturers have some great lenses, and some of the lenses by Nikon and Canon aren't necessarily the best.
I generally recommend that if you're looking for a particular focal length, aperture, or other feature, compare the various lenses that meet your needs. Based on review sites such as DPReview and Fred Miranda, you can make an educated decision about your particular need.
If your interest is primarily the optics, you need to look at individual lenses, not brands as a whole. You can't depend on a Nikkor (or Canon, Pentax, Sony, etc.) necessarily being sharper than something like a Sigma, Tokina or Tamron.
OTOH, unless you're pretty sure you're buying a lens to keep it forever, the third party lenses don't seem to be nearly as good of an investment. Just for example, years ago I bought (at just about the same time) a Minolta 35/1.4 and a Tamron 70-210/2.8. If I recall correctly, paid about $350 for the Minolta and about $750 for the Tamron. If I were to sell them now, I'm pretty sure those prices would be roughly reversed; getting $750 for the Minolta would be easy (in fact, $900 would be fairly reasonable), but I'd probably have a hard time selling the Tamron for more than $300 (and $250 wouldn't be particularly surprising).
As always, the answer is to choose carefully!
From experience I can say that although both Nikkor lenses and Sigma lenses cover a range of quality and price, Sigma covers a wider range. By that I mean that the worst Sigmas are quite bad and the top ones are absolutely superb. My absolute favorite Sigma for example is the 100-300mm F/4. It is extremely sharp, fast and nearly distortion-free.
Tamron could be similar but I've only seen terrible ones and mediocre ones so far. Most people seem to go for that brand based on price alone.
So, what you must do now is compare a specific lens from Nikkor vs specific ones from a third party brand. Note there are other differences than image quality, such as the focus motor performance, stabilization effectiveness, body compatibility (Sigma and Tamrons tend to require more upgrades when Nikon updates camera bodies) and - as silly as it may seem - the direction you have to turn the zoom and focus rings (it can drive you crazy if one lens turns 'backwards' compared to your other ones).
Finally, you forgot Tokina. Unlike Sigma and Tamron which makes most of their money selling low-quality lens and very low cost, they actually have only (9) lenses with some unique specifications and are generally of high quality. The Tokina 11-16 F/2.8 for example is extremely well-regarded.
I think the question is a bit subjective, however, I will say that Nikon makes some very, very, good lenses and at the high end they are hard to beat. Sigma and Tamron also make some very good lenses, including some that nobody else has (for example, Sigma has the widest rectilinear lens on the market for SLRs at 8mm). And all three make lenses that are, well, base consumer grade that aren't really very good at all.
Net effect, there is no general answer to the question, because it depends on which lenses you are comparing, and when you do that it is best to find a lens review site and check the performance vs cost benefits to determine which best works for you. At that point, I think you will find that it's sometimes a Nikkor lens and sometimes it is Sigma or Tamron.
So, if you are contemplating a lens option, it might be better to restate the question with some specifics. As it stands, the question is so broad and general that we can only give you a broad and general answer.
It depends on the lens. Look at reviews: Where can I find reviews of lenses?
I have a few Nikon lenses, and a Sigma 10-20mm for super-wide shots. When I was looking to get a wide lens, I researched the options, which included the Nikon equivalent (at the time) the 12-24mm. (they've since released the 10-24mm).
My research indicated that while first-party gear may be slightly better quality, the reality is that the difference is pretty small. I decided the extra cost of the Nikon wide wasn't worthwhile, plus it wasn't as wide, so I got the Sigma.
My point: in general, first party lenses tend to have somewhat better build/photo quality, but at an extra cost. Third-party lenses seem to be pretty competitive on both cost and quality,Sigma at the least. You need to decide if the extra cost is worthwhile to have all your lenses coming from the same company.
Reading reviews about the specific lenses you're interested in getting. The Digital Picture does very thorough reviews of Canon lenses.
I have had a number of Canon lenses and a single Sigma lens, their 20mm f/1.8, which also comes in a Nikon mount. The review from the aforementioned site summarizes my own findings well — for the (relatively cheap) price, the Sigma lens is decidedly ok at what it does. The biggest complaint I had was that it opens to f/1.8 but things aren't very sharp until you get to f/2.8. This is in contrast to something like the Canon 50mm f/1.4 (their mid-range 50mm), which is usably sharp at f/1.8.
One more thing you can do is rent lenses from a place like Borrow Lenses.
I used Sigma and Nikkor lenses. I can say the quality built of Nikkor is better than Sigma. But Sigma offers cheaper lenses with subtle quality difference. If you are rich enough just go for Nikkor, you won't go wrong and lessen your worries. If you compare the price between the 2 same specs and find the differences not worth it, just get the cheaper one.
The only way to do is to compare 2 specific lenses and read the data and MTF charts for each of those lenses.. I use photozone.de to get all my info for a price estimate, feature comparison etc before deciding on a lens.