Like most things it's a matter of preference. If you are looking for ways to improve your process then yeast nutrient is one of those ways. Of course there are many other things that most people would put ahead of it, but it is a good thing to do and is inexpensive. I just used it for the first time on this belgian quad i brewed recently. I made a starter and added it to that. If you're not making a starter you can just add it in the last 10-15 mins of your boil.
This is a good question and one that demonstrated the importance of understanding the metabolism of yeast cells.
If the wort will not contain some minerals or nutrients found in yeast nutrient, then it's a good idea to add it. I generally use it when making beers with many adjuncts as most of the nutrients yeast require are found in malted grains.
It's not just a question of availability (malt-based wort does have all the nutrients the yeast need, though zinc is usually limiting), but also how labile, i.e. how easily available those nutrients are to the yeast. That's where the nutrient comes in - it provides the nutrients in a more accessible form to the yeast, helping them through the lag and growth phases faster.
I'm essentially still a brew n00b but I would definitely recommend it. I have seen much better attenuation rates as well as less fermentation lag using Wyeast's nutrient. The bang for your buck is much higher than investing in equipment such as a fermentation chamber and temperature control. Not saying that you shouldn't invest, but when your other half has severely restricted your brew budget like mine has, then its worth the couple of bucks!
Yeast nutrient is not "necessary" for most beer fermentations. As others have said though it will help produce a faster, healthier fermentation. And that = better beer.
I started using yeast nutrient in about my 3rd or 4th brew and never looked back. With the Wyeast product, the cost is literally less than $10/year, and it could only possibly help. I can't fathom a valdi argument against using it... I use the recommended 1/2 tsp in a 5g batch and around 1/8 tsp in my starters (which average about 2L)